The argument that the Constitution, statute, or rule says so loses about 90% of the time in front of the US Supreme Court.
Au contraire. His questions was a simple one that needed a simple answer.
As a comparison:
Lawyer stands up in front of SCOTUS and says, "Now why on earth would we NOT require a criminal defendant to testify at his own trial?" Would be easily answered with, "uhhhhhhhh, because the Fifth says so?"
I think, in the very least, the "burden" is on the "jurisdiction" guys. The easiest reading of the 14th is that being born in the US = Citizen, and those who argue it means something else need to carry that burden. Especially considering they are attempting to strip away rights that the status quo says they have.