That is quite a theory, but I do not think it gets you into a courtroom.
That's right. The best anyone can muster is hearsay, innuendo and what could loosely be described as circumstantial evidence. This is the problem. American law presumes the affirmative. The onus probandi lies with the plaintiff, not the defendant.
As an example, in a civil case regarding paternity, it's the plaintiff (who is presumably suing for support) that has to prove that the defendant is the father. There's is no burden placed on the defendant to prove he isn't the father.
Obama has the upper hand, insomuch as the document that he already posses and that has been publicly validated be state of Hawaii officials qualifies as prima fascia evidence of his birth in HI. The mountain that the plaintiff's would have to climb, would be enormous.