In terms of game day security, no. The city has to cover the costs, which are pretty high. Now, I do think they can cut back on a lot of the stuff they do and some manpower, but I doubt anyone would sign off on that. But as an example, the officers working the game have to buy their own food at concession stands if they want to eat. That's dumb, and cheap on UA's part when they could give them vouchers for hotdogs and chips.
As far as the city taking liberties and trying to take advantage of UA, I'd be shocked if they don't. They tried to do it with this alcohol stuff but Byrne called them out. But that stuff should be handed on a case by case basis, and yes, the city of Tuscaloosa would basically be Phenix City with a different river if not for The University. They'd do well to keep that in mind.