The school can engage in an elaborate game of chicken with Ollie if it wants to, but it will be at its own peril. Once it gets ugly enough privately for either side to seriously contemplate filing suit, it blows up in everybodys' face if that happens. The moment anybody files suit it suddenly all becomes public record. Nobody is going to take that incredible PR risk. I doubt the school would be comfortable with rattling any sabers because even if they think they're doing that totally privately, word always leaks out and the school knows it.
Ollie will get whatever buyout amount he's entitled to in accordance with his contract, if and when that time comes.