Seems to me he didn't get fired for violating HIPAA, he got fired for bringing bad press to the Empire.
Of course, we'd need the details to confirm that. If he posted an address, a name, whatever, I have no sympathy for him.
If he said "I transported a rape victim today and I felt bad, maybe women should carry guns to protect themselves," I'd say fight it all the way. Since the police say he didn't violate any laws (HIPAA being a law), I'd say this is probably the way to go.