The concept of a "natural-born" citizen comes straight from English law which is why the Founders found no need to redefine it for us.
The concept of "natural born SUBJECT" comes from English law, and it is distinctly incompatible with the characteristics of citizenship.
Natural born Subject is to Natural born Citizen what a King is to a President.
They are two completely different systems of governance, with two distinctly DIFFERENT manners of regarding their individuals.
Really, I didn't know that the British had citizens.