You just brought up a great point. If the doctor is still alive you know he’d want the world to know that he delivered the baby who went on to become president. Or his children would tell it. How about nurses who worked at the hospital. There are many ways to confirm someone’s birthplace. And witnesses would be a good one. But I haven’t heard anyone come forward.
No, the doctor (probably deceased) wouldn’t have remembered this particular birth at all. Judge Bork had no recollection of two of his former law school students: Bill Clinton and Hillary Rodham, who made such little impression that he couldn’t remember them.
That used to be true, before the HIPAA law's privacy rule which went into effect 1n 2003. Now it's a crime to release "protected health information" punishable by hefty fines and possible prison term. So if the doctor or nurse are still alive, and if they remember one delivery out of thousands, they'd be very foolish to speak out.