“...seems oddly unwilling to disclose his birth certificate.”
Maybe it has nothing to do with citizenship; perhaps parentage.
Hmmmm. Would anyone care if he was a bastard? A goodly fraction of the electorate is, or is close to someone who doesn't even know who their 'baby daddy' was.
If his male genetic source is listed, who would it have to be for anyone to care? We're not a society that holds the sins of the fathers against the children.