Okay, then, it appears we agree. The Founders wrote the NBC requirement to assure that in the future of the Republic, the occupier of the highest office of the land would be a citizen born and bred of American parents.
I do not believe the Constitution as originally passed expressly required both that a person be born in the U.S. and that both of his/her parents be U.S. citizens as well. That is open up to reasonable disagreement because the Founders did not define what they meant by "natural born citizen".
But I'll state again, whatever the Founders original intent was in 1787, the ratification of the 14th Amendment in 1868 -- long after all the Founders were dead -- eliminated any pre-existing requirement that both parents be citizens. Under the 14th, you are a citizen at birth if born in the U.S. and subject to its jurisdiction. That's as opposed to a "naturalized" citizen who only becomes a citizen after birth, and therefore is not a "natural born citizen".