That doesn't cover people born to parents who had been born under the colonial regime. Either the Founders made an obvious boner, or the proposed definition of "natural-born citizen" is incorrectly narrow. I go with Door Number Two.
Now suppose someone were born in the US after the adoption of the Constitution, but his parents were born in the colonies during the colonial regime or perhaps the Articles of Confederation period. Such a person would qualify under the Vattel definition above, because the parents - having been citizens of the colony in which they lived - would have been "upgraded" to citizens of the United States (via congressional legislation, I'd presume) and would have been citizens of the US at the time their child was born. So there was no gap or boner or oversight on the part of the Founders. No one could have been excluded from the Presidency merely via a technicality arising from the change from sovereign colonies or states into the federal constitutional system.