...schools will ask you for many things that you're not obligated to answer. Your med school is not your doctor. Your med school is not a licensing board. (Also, despite how friendly the faculty may seem, your med school is not your friend.) Your med school is not entitled to your PHI. Frankly, I don't see what use they could have for that information that benefits you.
& in this day & age, the idea of needing that info to provide a medical history in case you need emergency care while at school & can't communicate yourself isn't even relevant. You'll likely access routine care via the hospital network affiliated with your med school, & that's the same network that you'd be taken to if you needed emergency care. In that case, the ER will already have access to your EMR. They won't need it from your medical school.