Just because one of the members of Hudson University's disciplinary committee is a psychiatrist doesn't make the student's testimony privileged. Doctor-patient privilege only applies when a person is talking to their doctor in private, a person talking to their doctor, or any doctor, with multiple other persons present in the room nullifies any expectation of privacy.
Misoprostol does not treat erectile dysfunction, and it also has a number of side effects that would be undesirable while having sex including abdominal pain, nausea, flatulence, headache, dyspepsia and vomiting. Being a second year med student Chuck Mills would know this making it truly ridiculous for him to try and explain away taking Misoprostol to treat his ED.
Chuck Mills couldn't have just bought Misoprostol from a pharmacist, it is only available via prescription in the United States. Misoprostol being dangerous for pregnant women is the main reason it is a prescription only medication in the US.