The obvious rejoinder is: no categorical proof of a negative is logically possible. The simpler way to state it is that this “concern” is no more than a mirror image of the “Bush is a deserter” bullshit from 6 years ago.
I’d say that doubts about the next President’s constitutional ability to hold the office are of a different quality than that. Especially since it would be so easy for Obama to put all of this to bed if he has nothing to hide. Every American should be asking the question: Why won’t he just release the birth certificate?