"Publius Huldah", here, correctly making the proper distinction between citizens, and natural born citizens who are eligible to be president:
In § 214, Vattel states that “fundamental law” may withhold from naturalized citizens some of the rights of citizens, such as holding public office. The Constitution is our “fundamental law”; and, following Vattel, Art. II, §1, cl. 5 withholds from naturalized citizens (except for our Founding Generation which was “grandfathered in”) the right to hold the office of President.
Remember! None of our early Presidents were “natural born Citizens”, even though they were all born here. They were all born as subjects of the British Crown. They became naturalized citizens with the Declaration of Independence. That is why it was necessary to provide a grandfather clause for them ["or a Citizen of the United States, at the time of the Adoption of this Constitution"]. But after our Founding Generation was gone, their successors were required to be born as citizens of the United States - not merely born here (as were our Founders), but born as citizens.
And do not forget that the children born here of slaves did not become “citizens” by virtue of being born here. Their parents were slaves; hence (succeeding to the condition of their parents) they were born as slaves. Black people born here did not become citizens until 1868 and the ratification of the 14th Amendment.
So! Do you see? If Our Framers understood that merely being born here were sufficient to confer status as a “natural born citizen”; it would not have been necessary to grandfather in our first generation of Presidents; and all the slaves born here would have been “natural born citizens”. But they were born as non-citizen slaves, because their parents were non-citizen slaves.