Actually, I believe the case (going from memory) was one to determine custody, or visitation rights. Paternity had already been established or stipulated to, and the plaintiff was not the biological father.
No, I've never practiced family law - of any kind - but, I suspect you might not have a lot of experience in federal court. The rules for "Proving an Official Record" are quite clear. A certified copy of a Certification of Live Birth more than meets the federal standard.
Of course, this is all just wild and meaningless speculation as one of these cases would actually have to be heard on it's merits for this to be relevant. I don't believe that's very likely.
All this “wild and meaningless speculation” would be cut short by the release of the vault copy of his birth certificate.
So, if anyone is to blame for all this wild speculation, its Obama.