Doesn't that contradict Vattel's definition?
Actually no, in fact it holds the Law of Nations/Nature in its purest form. That is, that citizenship is derived by heredity from the parent, not that of the soil which is the feudal definition. Natural law as laid out in the law of nations was & is the code of International law but not all countries held fast to it as they do today. Even merry ole England has now dropped their feudal form and changed their laws to state that children born to aliens are not English citizens at birth.
However, during the revolution, it was England's feudal definition that had to be contended with. American citizens who traveled to England and other countries that still practiced feudal citizenship were subject to having foreign citizenship forced upon their children born there. Those children were registered and during the war of 1812, the Brits would board ships and any male found to have been born in England, regardless of parentage was taken and forced into the British Army. But is wasn't always that way. When England was founded, it was the citizenship laws of nature/nations that was originally founded and that is the ancient laws the founders spoke of and the laws they put in place for the new country.
Yes, of "natural born citizen" at least, except in the case of children born to military or diplomats serving the nation, but outside of it. It may have been an attempt to extend just plain old citizenship to such persons, and later they realized they had overstepped in trying to define a Constitutional term. In fact in 1795 they dropped the "Natural Born" language when they repealed the 1790 and replaced it. The language is thus no longer in effect and has never appeared again in the statutes. The relevant part of 1795 Naturalization act follows.
(It's in Section 3, on the next page.)
...; and the children of citizens of the United States, born out of the limits and juridiction of the United States, shall be considered as citizens of the United States: Provided, Theat the right of citizenship shall not descent to persons whose fathers have never been resident in the United States.
Vattell however would have such persons be born citizens:
From Law of Nations, Book I, section 215:
It is asked whether the children born of citizens in a foreign country are citizens? The laws have decided this question in several countries, and their regulations must be followed. By the law of nature alone, children follow the condition of their fathers, and enter into all their rights (§ 212); the place of birth produces no change in this particular, and cannot, of itself, furnish any reason for taking from a child what nature has given him; I say "of itself," for, civil or political laws may, for particular reasons, ordain otherwise. But I suppose that the father has not entirely quitted his country in order to settle elsewhere. If he has fixed his abode in a foreign country, he is become a member of another society, at least as a perpetual inhabitant; and his children will be members of it also.
Of course BHO Sr, did no such thing, He did not "quit his country", but rather returned to it after completing his educatoinal sojurn in the US.
It does but not for the Presidency. The President must be born here of parents both of whom were also born here.