He's a campus police officer. Just as in Indiana, he's a certified peace officer with police powers, but instead of being employed by the city, he's employed by the university (that is, the state) There's no dual employment in this case. I agree with you, though, if he was a city cop and moonlighting/doing security work for the university but not AS a cop, he should have to choose one or the other. (Case in point: A couple of the EMTs and medics I supervised at my last station were also cops/coroners/similar. If they're on the medical call, they can't act as a coroner. If they discover info as a medic, they can't arrest or otherwise use the info they found, as a cop. They can, however, as a cop, do medical stuff, to a point, as long as the medical director allows it.)
There is a dual authority though. In this case the "police officer" had not reason to arrest the man so he issued him some kind of disciplinary report from the school. Do cops who moonlight at High schools make it standard procedure to carry detention slips?
In the case that I am talking about in Vincennes,VUPD would never bother with a search warrant for a dorm. They would simply ask permission to enter and if refused they would say that are a school employee and are allowed to enter at any time as such. This was my experience as a resident assistant and while I never saw them abuse this I still question the legality of using the badge and uniform to uphold a school/private company/churches "house rules"