I’d agree with everything you say if Obama were in fact a natural born citizen, but as a matter of fact and law, he is not. You say he is, with whatever logic, I do not know, I say he is not: We disagree.
The courts have an OBLIGATION to fix this, as they must uphold the Constitution if the Constitution is to mean anything at all.
If the courts determine that any damn thing born in a catbox is, therefore, a cat, so be it. I cannot imagine they would rule so.
He is a natural born citizen because being born in the United States makes him so.