Not correct. That's not why "Obama" released whatever it was that he released. He is under no obligation to prove anything beyond what was submitted to or requested by the two Special Joint Sessions of Congress which met in January 2009 and January 2013.
There is one and only one forum designated and eligible to resolve this matter, and that forum has convened twice and ruled, without objection, that the man calling himself "Obama" was eligible and was in fact qualified and duly chosen to be President.
Unless this John Doe, whoever he really is, attempts to occupy his office beyond 12:01 PM on January 20, 2017, the matter is closed (as far as judicial processes are concerned).