So far as I know, the Constitution does not define terms.
The courts have given definition and meaning to many of the clauses of the Constitution. So far as I know they have not directly tackled the meaning of natural born citizen.
Absent some writing from the Framers as to the meaning of Natural Born in the Constitution, I would assume we then look to English Common Law at the time. It is my understanding that anyone born in the empire was a British citizen, unless they were born to a foreign diplomat.
This is just the most astonishing claim that I've heard in association with this issue. Not that you're the only one to have made it; you're not. But, it's just nonsensical.
It's Vattel who laid out the requirements for natural born citizenship in a constitutional republic. Samuel Adams, John Quincy Adams and James Otis are recorded as having cited Vattel's Law Of Nations as early as 1764. Benjamin Franklin held Vattel in very high esteem. Our first Chief Justice John Jay likewise.
The meaning of the Constitutional term of art "natural born citizen" was clearly known and understood by the framers; they had a copy of Vattel with them at the original Constitutional Convention.