That's not their definition. That's a new definition recently invented.
The founders intended that Presidents had to come from people already here at the founding, or people born here after the founding. They excluded "naturalized" citizens from eligibility because they were concerned that King George III would send over some noblemen to become citizens and run for President... and thusly nullify the revolution. The requirement for "natural born" in the U.S. was enough. They didn't ~need~ to require that their parents were also born here.
You are totally refuted in my post above. The one you declined to read.
David Ramsay refutes you.
John Jay refutes you.
The text (and editing history) of Article II, Section 1, Clause 4 refutes you. In Hamilton’s original draft, the constraint was that the President had to be “born a citizen.” In response to John Jay’s criticism regarding the need to prevent the Commander In Chief from having any foreign allegiances, loyalties or conflicts of interest, the constraint was changed to “natural born citizen.” So “natural born citizen” MUST be more restrictive than “born a citizen,” and must be so in ways that address Jay’s concerns.
It was only after the change from “born a citizen” to “natural born citizen” that the exception was added that permitted those who were citizens at the time the Constitution was adopted to be President. There’s no reason for any such exception unless the “natural born citizen” requirement so severely restricted who would be eligible that few could have satisfied the requirement.
And the Congress of 1813 refutes you. They passed a law requiring sailors on US ships to be “natural born citizens.” Because the British Navy was stopping ships at sea looking for able-bodied men who qualified as “natural born subjects” of the British Crown so that they could impress them into the British Navy. Anyone born on British soil (such as the American colonies prior to the peace treaty,) or born to a parent who was a natural born subject of the Crown when the child was born, would qualify as a British “natural born subject.” By requiring that sailors on US ships be “natural born citizens,” Congress sought to prevent the British the opportunity to impress US sailors, since any sailors born on US soil to parents who were US citizens would not qualify as British “natural born subjects,” and so could not legally be impressed into the British Navy.
References for all the above facts are in my post above.
Natural born requires both parents to be citizens, whether native born or naturalized, at the time of birth of their child. I haven't seen where the parents must also be natural born.