I can only speak for myself but I think this section is a lot more ambiguous than you think it is. I looked for the quote you cited but couldn't find it. So when you state we're talking about only the context Caleb is speaking about, I have little to go on. You define a few things "handgun skills" are not but don't tell us what "handgun skills" we're specifically assessing.
It was part of a much longer discussion that started off with Caleb saying: "
I wonder what percentage of dudes dropping $1,000+ into upgrading their Glocks have taken a class from a legit instructor..."
....much fun was had. Especially when someone added: "
Next question should be "out of those who have, how many are instructors like Sonny, Zero, Yeager, Pincus?"
Interestingly enough, it was someone else who initially brought up the shot timer thing.
In the same vein I don't know the context of Caleb's "serious shooters" with "serious handgun shooting skills." For example, are we talking about world class IDPA skills or the ability to hit a gong at 200 yards or Uncle Joe who has been shooting daily for 20 years and knows he's a lot better than he once was?
None of the above, really. More along the lines of "serious about increasing shooting skills" was the meaning I pulled out of it, as opposed to "reaching a certain specific level of skill".
This isn't about parsing what 'is' is as much as understanding what we're actually talking about. That's why my original answer was all over the place. I was trying to cover all bases. 
Oh, I thought you had a lot of good stuff in there. It was the people talking about things I specifically said it
wasn't about that didn't make much sense to me.
Having read your subsequent responses I think I understand the context and questions a little better.
Correct me if I'm wrong but by "handgun skills" you mean, draw, target acquisition, hits on target, safety, stance, grip, etc. And speed and accuracy are thrown in as well. For the sake of argument could we maybe simplify this and just say, 'The handguns skills necessary to compete in IDPA?'
I personally wouldn't have picked IDPA, actually.
But that's because while I shoot IDPA, I'm not really an IDPA guy.
In general, if someone is serious about pistol shooting---in other words, they take seriously the idea that they should work on their pistol skills---they are going to do certain things. They'll work on their accuracy, they'll work on their speed, they'll be able to handle the manual of arms for their pistol in a competent fashion, the gun-handling skills that go along with the part when the trigger is actually pulled will also be important...
Those things may be important skills for USPSA or IDPA, but they would also be important for pretty much any other application of pistol shooting (other than bullseye shooting, and some of those skills would ALSO be important there) including self-defense.
Would it be safe to say that a "serious shooter" is someone who regularly practices in order to better pistol handling skills?
I would go with that, with the caveat that it is hard to take someone seriously if they don't know what they are doing.
At ENGC, I often see people who obviously come to the range frequently. They show up, put a full-size silhouette at 3 yards, and draw and fire 4 rounds on it multiple times until they run out of ammunition. (What's really annoying is when they do this in bay 5, taking up the big bay when they could move to bay 1 so the rest of us can practice more long-range pistol shooting...but that's a separate issue.
)
Their draw is awful (fumbling and slow), their grip is poor (they juggle the gun once out of the holster to change their grip and then put the second hand on it) their draw is awful (yes, I know I am saying it twice but either they perform a bowling draw or a fishing draw, and both demonstrate little muzzle control), and their sight control and trigger control are....poor (taking huge amounts of time to sight in on a 3-yard target, then yanking the trigger so the target ends up eventually looking like a target shot with a shotgun that patterns badly).
Now, most people looked like that at SOME point in time. We all started both clueless, and skill-less.
However, I'm talking about people I've seen show up multiple times to practice. (Several of which, I've heard say the famous phrase "I've been shooting for 20 years, and I know...") These people aren't serious about increasing their pistol skills, because they haven't bothered to learn what that means, either the "skills" part or the "increasing" part (they haven't done any work learning what they need to do to increase their skills).
So....to me, someone "serious" about pistol skills is someone who not only works to increase their pistol skills, but has actually done enough research to have an idea 1) what pistol skills are important for their particular application, 2) what is considered "competent" or better yet "good" levels for that skillset, and 3) has done at least some basic research on how to learn and practice those things.
There's a couple of older gentlemen who come out to the pistol bays at ENGC regularly to practice pistol shooting ("for combat," they told me "not that competition stuff, we have different rules" they said when I told them that no, they could not share the bay with me because they were handling firearms behind the shooting line and sweeping several of us multiple times as they were back there). I'm not going to describe them more, as that isn't necessary. However, I have seen them out there quite often, for several years.
They are no better now then they were the first time I saw them several years ago. They still do exactly what they did originally, and their safety habits, sight control, trigger control, and gun-handling skills are unconsciously incompetent--in other words, they don't even realize how poor their control IS.
They probably think they are serious about pistol shooting. They aren't. They have shot a lot, and shoot regularly, but that isn't the same thing.
"Serious handgun skills" needs to be defined. Sticking with the IDPA theme, as Novice level, pretty much anything above Novice is "serious skill" to me. But in the context of your discussion, do you mean Expert, Master...?
Not really. I know a number of C-class shooters that are serious about pistol shooting. They don't have high-level skills (not yet, at least), but they are serious about increasing their pistol skills. They are dedicated to practicing, they actually have a plan for getting better at specific skills, periodically they test themselves to see what has improved and what hasn't...their skills are going to increase. At what rate, I don't know. But they are going to get better....and probably at least eventually make A-class or so.
...I realize reading that again, that instead of talking about "serious skills" I'm talking about "serious about skills"...
...but I'm trying to think of anyone I know who was serious about skills who didn't end up eventually having serious skills. Which, thinking about it, I wouldn't consider world-class, or national-class, or even necessarily regional-class, because to my mind "serious skills" isn't about how many other people you can beat in a competition.
Hm. How to say this....
I think that, to me, "serious skills" means getting to the point of unconscious competence with respect to the fundamentals of shooting and gun-handling. Consistently, your times will be fast and your accuracy will be good; draws, reloads, and remedial actions will occur without issue or error, even in situations in which other things are going on.
One of the things that keeps happening to me almost every time I take a class (Rogers Shooting School, Southnarc's ECQC, Tom Givens' Instructor Development course, etc) is that at some point in time during a complicated shooting drill where people have to perform gun-handling and shooting actions while simultaneously doing something ELSE not gun-related (whether mental decision-making or physical additional actions) the instructor says to me "Hm. Competition shooter?"
And when I say yes, and ask why, they always say some variation on "you've practiced enough so that you don't need to think consciously about the shooting part, so you aren't having a problem doing the other things we are asking you to do."
Seriously, that's been said to me in all but one of the last 5 classes I've been in. (And that one wasn't a shooting class, it was an unarmed defense class.)
That's paraphrased, obviously, and plenty of people get to that point
without being competition shooters. (Though it is certainly true that one of the easiest ways to stay motivated to practice more is the
fun of competition.) Those three instructors (and several others) could see very quickly who in their class had been serious about shooting, because those people were the ones who practiced to get to an unconscious competence level. In the class with Tom Givens, we even had an extended discussion about it, because this was the Instructor Development class and so we got him to speak more about what he has seen regarding practice and mental practice, because he mentioned that same sort of thing (having enough free mental processing ability to problem-solve easily while shooting) for several people, and we all talked about our backgrounds a bit in terms of practice.
I can't quote him exactly because I don't remember his precise words, but it was along the lines of "people who think pistol skills are important work on being good enough so that they have plenty of time to think about the other things while shooting" (he was discussing things from a self-defense perspective, wherein the ability to problem-solve and make appropriate judgements is REALLY important....so most of your mental processing will be taken up by that).
So...I don't personally really think of "serious skills" as something you can judge by having a draw speed of less than one second to an A-zone hit at 7 yards and a speed reload time of under 1.5 seconds and so on.
(Which is good because my reloads suck and that would hurt my little feelings.
)
Sure, people with serious skills will ALSO be fast and accurate...but that's because to get to a level of unconscious competence in shooting skills and gun-handling, the practice they have put in will ALSO increase their skills to a pretty high level. But the actual level itself is a byproduct of the practice necessary to reach unconscious competence.
Does that make sense? I realize I'm all over the place here.
So to answer your two questions immediately above, assuming skills in the upper echelon, no I do not think serious shooting skills can be obtained without at times using a timer.
I have never known anyone with serious shooting skills that didn't use a timer. Not that I know that many. 
I've run into and seen quite a few, though "knowing them" isn't how I'd characterize it. (I know who
they are, they probably wouldn't recognize me at all other than "the CRO who runs the hard memory stages all the time at Area 3" or something like that.
) I'm a decent shooter, but it is really cool sometimes to see what world-class shooters can do.
What's interesting to me is the probably one of the most "serious shooters" I've ever met, who pretty much every single day works on his own shooting, works on how to shoot better and practice better, and works on how to teach people how to shoot well better, not only uses a timer for just about everything, but also has some of the most stringent timer requirements of anyone I've ever met. (That would be Bill Rogers. The Rogers Shooting School tests are some of the most difficult, time-based ones I've ever tried in my life.) He isn't a competition shooter, though for awhile he competed and was extremely good. Most of his life he's been training other people to shoot really well, most of whom were private classes for the military and law enforcement.
To me "serious about shooting" can be defined as someone who practices with the intent to improve. But unless I'm wrong, what you're asking is more along the lines of, 'How do you define serious practice?' If the latter is correct, I would define it as someone who diligently practices to the best of their ability and situation. The practice is focused toward building and maintaining fundamental skills with the goal of increasing speed and accuracy. And yes at some point the individual will need to use a timer to continue progressing.
I added the emphasis in the above quote, because additionally I tend to think that someone who is serious about shooting will ALSO be someone who has actually spent some time researching or learning HOW to improve.
It continually amazes me that people will run to an indoor range, blast off a box of ammo into a single silhouette target at 5 yards one full magazine at a time, leave, and consider that good practice. We know SO MUCH MORE about how to get better at pistol shooting, but.....some people aren't serious enough about actually improving their pistol skills that they actually take the time to look at what they should do to be better.
What do I consider serious skills? That's a wide open question but to bring more focus I'll go back to the IDPA context and say Expert and Master.
My opinion about that really ends up being that if they are serious about increasing their pistol skills, they'll end up (from a competition perspective) at least A-class in USPSA, and EX or MA in IDPA, assuming basic eyesight and hand-eye coordination. Assuming they compete.
But like I said, that is a
byproduct of the practice they do while reaching the level of unconscious competence---which is kinda what I think I personally believe to be the goal of most people who are "serious" about pistol shooting. (They might not think about it that way, obviously.) They may never do any competition shooting at all, so rating their skills in that fashion isn't going to work.
