And why in the world is the shoe on the wrong foot in this scenario?
Do you think the founders intended that critics would have to prove someone not a citizen, or do you think they expected someone claiming to be one to prove it?
Why is not the burden of proof where it belongs? On the person who is seeking office?
When Roger Calero ran for President back in 2004, they kicked him off the ballot. Since he couldn't prove he was a US Citizen, this was a completely rational thing to do.
But now we've flipped our sanity by arguing that the candidate doesn't have to prove it, his critics have to prove he isn't!
What a bunch of crap.
The burden IS on the one seeking office. The text of the Twentieth Amendment clearly places this burden on the President-Elect.
"If a President shall not have been chosen before the time fixed for the beginning of his term, or if the President elect shall have failed to qualify"
If the President Elect fails at something, it is an action of his, not others. He tries to qualify and succeeds or he tries to qualify and fails.