If it's at all like the Big 10 agreement, then I'd say it's likely you shouldn't use it. If I remember properly, the big 10 agreement is fine for faculty and staff (and spouses) regardless of purpose, but students are restricted to official business (and it might be grad students only, can't remember).
Oh, and FWIW, if something happens, they very much will look into it. We had an issue and because it was my wife that rented the car, when national contacted the university they said she wasn't an authorized user because they apparently couldn't match her up to me. I had to track down the person at the university responsible for those claims and she was then able to pass on to national that it was indeed an authorized user.