Mechanics aside.
The records are there. It’s what governments do.
Now whether individuals with the government share those records, or lose those records, or change those records is another question.
We’re talking about Obama, after all.
His shit just keeps disappearing!
Employees who have merely looked at celebrity records have lost their jobs; one got a four month sentence just for looking. One employee who sold information to the press was facing a 10 year prison term, but died before she could be incarcerated. Hospitals guard protected health information carefully since HIPAA, sometimes absurdly so.