Any person who possesses a firearm in a school, on school grounds, in a school-owned vehicle, or at a school-sponsored activity or athletic event is guilty of the offense of unlawful possession of a firearm at a school. Unlawful possession of a firearm at a school is a Class IV felony. This subsection shall not apply to the issuance of firearms to or possession by members of the armed forces of the United States, active or reserve, National Guard of this state, or Reserve Officers Training Corps or peace officers or other duly authorized law enforcement officers when on duty or training,
What this says is that a Peace Officer with an issued or authorized firearm is exempt.
What it also says is that OTHER duly authorized law enforcement officers must be on duty or training.
Read it like this; Shall not apply to the issuance of firearms to or possession by peace officers.
If you read it using only one category at a time you should understand what I am saying. The use of the OR's simply replaces comma's.