"Scotland Yard" was originally the Scottish ambassador's residence and was considered Scottish territory (back when Scotland was a separate country).
I'm sure this was done with the "natural subject" issue in mind.
It was considered at one time (circa 1793) that the children born overseas of U.S. citizens would be ‘Natural Born Citizens’. It was repealed in 1795.
Children born overseas of U.S. citizens are born ‘jus sanguinas’, or citizen by blood, and are citizens by statute. Children born in the U.S. to non-citizen parents or just one U.S. citizen parent are ‘jus solis’, or citizen of the soil. There are legal statutes determining those types of citizenship.
There is no statute for “Natural Born Citizen” because it is natural law - that a child born in a country to citizen parents is a citizen is unquestionable. No statute needed. Our founders knew what the definition of a natural born citizen entailed.
One should keep in mind that there is no right to be President. “Natural Born Citizenship” is a circumstance of birth that only applies to the elegibility requirement to be President - nothing else. It is a form of national security to prevent a President with split allegiences.