You said it much better than I.
You have a way of making your point.
What Im thinking is that the CIA might have, or might now make it their business to acquire, birth certificate docs and/or for example, college docs showing Obozo registered as a foreign student in the US, etc etc. Then they might just hold such docs and find a surreptitious way to release them (w/o their fingerprints, of course), at a strategic time, say during Zeros re-election campaign.
Just hopin anyway ..