My point was just that it could have been obtained many ways, such as via a nice payment to one of the relatives he's thrown under the bus.
I think he was clearly born in Hawaii, but has something embarrassing on there.
The laws actually provide for a new birth certificate to be made to cover up the “embarrassing” situations - illegitimacy, gender ambiguity or change, adoption - with the original one containing the embarrassing information being sealed. So none of those things would require an amendment, nor would an amendment be apparent to anybody looking at his documentation.
So if it was something embarrassing it would have to be something besides those things.