You raise the questions I wondered about. I have to get medical records for clients in my work. To get ANY info, I have to have a signed HIPAA-compliant authorization for release of confidential information.
If I’m looking for records from more than 5 or 7 years ago, they have to be retrieved from the hospitals’ archives. They wouldn’t show a patient from 1961, much less divulge any information on whether the person was or was not a patient without authorzation. If they did they would be subject to enormous fines.
If they divulged information on an actual PATIENT, they could get in trouble. But if they say that they can't find anything on 0bama (since he wasn't born there) he was never a patient and is not protected under the doctor/patient privilege.