Hmm... so what's the deal with the, for lack of better terms, ex-parte hearing Yale put her through?
If the hospital is an unrelated medical institution, how did her medical history get released to the school? Is this even legal?
Also, IIUC, the psychiatrist who told her "we can't have you here" was employed at the hospital, not the university?
In short, there seems to be some type of relationship between the hospital and the university.