But did he really? Stop and look at the exact quote cited:
"The natives, or natural-born citizens, are those born in the country, of parents who are citizens."
Birthers automatically treat "of parents" as meaning "each of two parents." But that is not a given. The subject ("natives") is plural, so it stands to reason that "parents" should be plural too. While grammatically correct, "The natives...are those born in the country of at least one parent who is a citizen" is more than a bit stilted.
Vattel points out in his next sentence that "children naturally follow the condition of their fathers." So it would be perfectly accurate to rephrase the above Vattel sentence to read:
"The natives, or natural-born citizens, are those born in the country, of fathers who are citizens."
Fathers. Plural. Now, does that mean that a "natural born citizen" must have multiple fathers? Of course not. But multiple children must have multiple fathers; similarly, multiple children must have multiple parents.
As a point of comparison, consider the Sons of Confederate Veterans. How do they describe themselves?
"The SCV is the direct heir of the United Confederate Veterans, and the oldest hereditary organization for male descendants of Confederate soldiers."
"of Confederate soldiers." Does this mean that to be a member, you must be descended from more than one Confederate soldier? Obviously not. (Though I would still qualify, being descended from five.)
Similarly, there's the United Daughters of the Confederacy. They write:
"Membership is open to women no less than 16 years of age who are blood descendants, lineal or collateral, of men and women who served honorably in the Army, Navy or Civil Service of the Confederate States of America, or gave Material Aid to the Cause."
"of men and women." So read as literally as Birthers read Vattel, not only must a Member be descended from multiple Confederates, rather than just a single one, but this says she must be descended from both Confederate men AND Confederate women. While, when taken in the context of other pages from the website, is clearly not the case.
This same tortured reading applies to virtually every 'two-citizen-parent' citation that Birthers have. Vattel, taken in context, reflects a definition of "native" that is governed wholly by the father's citizenship status, without regard to the mother's. It is a definition from a bygone era. If the Birthers wish to claim that in 1961 America, a child could be born whose citizenship and eligibility for the Presidency was governed only by the child's father and with no consideration given to the mother, then they should be upfront about it.