Military troops are usually "armed" in the sense that they have been issued duty weapons (firearms). Most every stateside infantry barracks is chock full of rifles. It's just that the troops don't get access to or possession of any ammunition without some kind of serious need, like at a fire base in a combat zone. Ammo is usually very carefully controlled unless the Bad Guys are just beyond the concertina wire.
First time I ever pulled guard duty was somewhere wayyyyyyyyyyy out in the remote California boonies in the darkest black of night. Carried a rifle w/bayonet. Not one single round of ammo was issued nor allowed to me. Woulda been better off with a baseball bat. Maybe with a big spike nail in it.
Military experience shows that when troops have both guns and ammo, random gunshot wounds proliferate. And suicides.
MPs on duty have ammo. But then, they are the Cops.