http://faculty.maxwell.syr.edu/jyinger/Citizenship/history.htm
Madison did not record any debate on this clause. Instead, on August 31, the Convention referred various issues, including presidential qualifications and the method of electing the President, to a Committee of Eleven, which had one member from each state.(31) This committee presented its report on September 4, 1787.(32) The words “natural born citizen” first appeared in this report. Indeed, these words appeared in a form that is identical to the final version in the Constitution: “No person except a natural born citizen ... shall be eligible to the office of President.” The record of the Constitutional Convention provides no explanation for the introduction of the words “natural born.” On September 7, “The section requiring that the President should be a natural-born citizen &c, & have been resident for fourteen years, & be thirty five years of age, was agreed to nem. con.”(33)
There is a reasoned discussion of how a letter by John Jay might have have influence on the final wording.
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In that discussion it refers to The Naturalization Act of 1790 which states in part:
And the children of citizen of the United States, that may be born beyond sea,Also, children of citizens born beyond sea, &c. or out of the limits of the United States, shall be considered as natural born citizens: Provided, That the right of citizenship shall not descend to persons whose fathers have never been resident in the United States:Exceptions. Provided also, That no person heretofore proscribed by any state, shall be admitted a citizen as aforesaid, except by an act of the legislature of the state in which such person was proscribed.
This act of 1790 was replaced by the act of 1795 and the wording of "natural born citizen" was removed. This tells me that those in government at that time understood clearly the meaning of the phrase and it's significance in insuring undivided loyalty.
It's certainly possible that those who passed the 1795 Act may have intended, by the change in wording, to exclude children born abroad to US citizens from Presidential eligibility.
Let's grant the point for the sake of argument.
Even so, it doesn't change the fact that the First Congress, which (with President Washington) included 40% of those who had just signed the Constitution) intended for such people to be "natural born citizens," eligible to the Presidency.
That fact alone destroys the claim that it took birth on US soil plus two citizen parents to make a natural born citizen, or to make someone eligible to be President.
And that action has the stamp of approval on it of 40% of the signers of the Constitution, which - aside from the Constitutional Convention itself - was almost certainly the biggest gathering of signers of the Constitution that ever took place.