Was there any other purpose in writing it? Was there any other reason to be considered as natural born?
I think it was just the popular term of art during that period. The current "buzzword" so to speak. Perhaps they meant it to convey an ability to be President, or perhaps they never really considered the possibility that it would be a modification of what were the then accepted standards of eligibility.
I know that the English law that says the same thing (and which was much older) uses similar verbiage.
I will however point out that none of these "Natural born subjects" would ever become the chief executive officer of Britain. :)