I don't understand why this is a bad thing.
Lawsuits are society's way of telling organizations, "don't let this happen again".
So, let's assume, yes, this college is worried about a lawsuit from the girl hurting others.
You assert, "those jerks, they're only focused on avoiding a lawsuit and covering their ass."
Well, yes, because society has told them "if you let this girl/other students get hurt because you ignored an obvious threat to their safety, their parents will sue the hell out of you".
So, in reality, the threat of a lawsuit is, by proxy, actually protecting the other students. How is that a bad thing?
(Frankly, I would give Yale the benefit of the doubt, and assume they were directly concerned for the safety of this and other students, instead of only concerned about the lawsuit, but, either way, the results are the same: no one got hurt, she got help she needed, and she's back.)