They are not rent-a-cops, they are state law enforcement officers, albeit bored.
Soooo. . .they are empowered with the same authority as state officers and enforce state and university laws.
In most jurisdictions, especially at public universities. But I really appreciate you pointing this out. A number of good friends are campus police, they go through the same training as municipal police and state police, often have higher qualifications (their jobs are highly sought after), have arrest powers throughout the state, have to deal with a poisonous hormonal soup of angst-filled 18-24 year olds day in and out, and then they have to put up with jokers who tell them they are not "real" cops. Do they have SWAT teams and attack helicopters? No. But the vast majority of municipal and state police deal with exactly the same mix of stupid criminal garbage as the campus cops do, at the same rate, and facing the same problems.
Thank you.