No they don't. You are simply repeating the bullsh*t that a lot of Pro-Obama people spewed when this issue was being debated.
Wong Kim Ark (which I am sure is the one you are referring to) never declared Wonk Kim Ark to be a "natural born citizen." It said he was a citizen by the operation of the 14th amendment, which is clearly not at all the same thing as a natural citizen.
So people are misleading others about what the Supreme Court actually said, and you should stop repeating this misleading claim.
And basing his theory on Vattel, who didn’t write what he thought Vattel wrote, is just bad history.
Uh yes, Vattel did write what he thought he wrote. Did I show you that Pennsylvania law book which explicitly said Vattel was the source of the definition for "natural citizenship" in the United States?
“Uh yes, Vattel did write what he thought he wrote.”
Simply, factually wrong. We KNOW what he wrote. “Les Naturels ou indigènes font ceux qui font nés dans le pays de Parens Citoyens.” That was dealing primarily with Continental Euprope’s laws, but it very plainly did NOT say “Natural Born Citizen”.
He DID discuss “Natural Born Subjects” elsewhere - forget where - but he was not even TRYING to define NBC.
AND...Wong Kim Ark discussed the meaning of NBC at great length. While it was “dicta” and not binding, it proved so persuasive that no court since has ever felt a need to question the meaning.
We have court cases going back to the early 1800s involving the meaning of NBC and they tend to go like this:
“The country where one is born, how accidental soever his birth in that place may have been, and although his parents belong to another country, is that to which he owes allegiance. Hence the expression natural born subject or citizen, & all the relations thereout growing. To this there are but few exceptions, and they are mostly introduced by statutes and treaty regulations, such as the children of seamen and ambassadors born abroad, and the like.” - Leake v. Gilchrist, 13 N.C. 73 (N.C. 1829)
“The term citizen, was used in the constitution as a word, the meaning of which was already established and well understood. And the constitution itself contains a direct recognition of the subsisting common law principle, in the section which defines the qualification of the President… The only standard which then existed, of a natural born citizen, was the rule of the common law, and no different standard has been adopted since. Suppose a person should be elected President who was native born, but of alien parents, could there be any reasonable doubt that he was eligible under the constitution? I think not. ” - Lynch vs. Clarke (NY 1844)