One way of thinking about whether medical school candidates' personalities should influence admission is to ask the question, "Would you want this person to care for one of your loved ones?"
Applicants to medical school are expected to live by their presentation of themselves and of their commitment to medical practice. It is not just a retrospective report but also a promise to which admissions officers should be able to expect them to adhere.
Writing a case study of a psychiatric patient may change the patient-physician dynamic even if the patient consents to be written about. And when the patient is a minor and consent must involve her parents, the process becomes even more complicated.