Anyone granted citizenship at birth by another nation - even if born to two U.S. citizens on U.S. soil - would be ineligible for the Presidency according to your ‘reasoning’.
Most of our founders were natural born subjects of England according to English law. England considered all Americans subjects of England - thus their impressment of U.S. sailors on the high seas - until the war of 1812 decided the issue.
Was any American born between 1776 and 1812 not eligible for the Presidency because England considered them as English?
It has nothing to due with law, you posited citizenship flows through the blood, ergo it becomes a birth right.
As Happerestt stated, a child born to two American Citizens on American soil is a NBC, there are doubts to the others.
You need to read the Constitution a little more carefully.
They specifically exempted themselves as they were Citizens at the time the Constitution was signed.
They were eligible, of course. It didn't matter whether England considered them English subjects or not.
And they didn't need to use the grandfather clause, either. All of those persons who had been born "natural born subjects" of the English king were, upon Independence, natural born subjects or natural born citizens of their State and of the United States.
I know this doesn't fit birther doctrine, but it's true.
The reason is (to put it simply) they were children of their local Colonies and of the King. We could say that the King was their father, and the Colony was their mother.
When the parents divorced, they went to live with their mother. They never stopped being natural born sons of their mother, and the fact that she changed her last name from "England" to "United States" didn't matter. They were still her natural born sons.
Nor did it matter that we changed the term used for a member of the nation from "subject" to "citizen." As both Judge Gaston in North Carolina and the US Supreme Court noted, the two terms were completely convertible. Yes, "citizen" drops the implication of obligation to a king. That's the only important difference.
The grandfather clause was put in place NOT for the sake of people like George Washington, but for those of foreign birth who had helped in our Revolution. Men like James Wilson and Alexander Hamilton (who was born in the Caribbean, and who probably would've later become President except for the unfortunate fatal duel with Aaron Burr, Vice-President of the United States.)
This understanding is affirmed by Father of the Constitution James Madison and by various important early legal authorities and historians, including Supreme Court Justice Joseph Story, James Bayard, Chief Justice John Marshall, Chancellor James Kent, John Seely Hart, George Bancroft, and the US Supreme Court.
Quite a few quotes from various of these authorities, that illustrate the fact, are here.