It’s like some of you guys totally forget HIPAA.
No, it’s not the same as with the NFL.
I don't think it would be HIPAA, because that law applies to covered entities. Unless you are the party providing care or an insurance company, it doesn't really apply to you. For example, a reporter who finds out that an athlete had a medical procedure and discloses it wouldn't be a HIPAA violation. If it was revealed that they found out about it from a nurse who leaked it, the reporter STILL hasn't violated HIPAA. It's the nurse/hospital that did.
But the law that IS likely in play is FERPA, and that does apply to schools, allowing them to withhold information about a student from release. A lot of schools use it as a shield to avoid disclosing information about athlete status. They don't want to disclose anything that they don't have to, if for no other reason than to prevent their opponents from knowing exactly what's going on.