I agree, and Ben Franklin was a huge proponent of Vattel, see links:
In Minor v. Happersett, Chief Justice Waite, when construing, in behalf of the court, the very provision of the fourteenth amendment now in question, said: 'The constitution does not, in words, say who shall be natural-born citizens. Resort must be had elsewhere to ascertain that.' And he proceeded to resort to the common law as an aid in the construction of this provision.” […]“At common law, with the nomenclature of which the framers of the constitution were familiar, it was never doubted that all children born in a country, of [169 U.S. 649, 680] parents who were its citizens, became themselves, upon their birth, citizens also. These were natives or natural-born citizens, as distinguished from aliens or foreigners.” .-Associate Justice Horace Grey, in US v Wong Kim Ark (1898)
From Wikipedia
Prior to Wong Kim Ark the Supreme Court had held that birthplace by itself was not sufficient to grant citizenship (Elk v. Wilkins, 112 U.S. 94, 1884). U.S. citizenship law since Wong Kim Ark has acknowledged both jus soli (citizenship through place of birth) and jus sanguinis (citizenship inherited from parents).
It would appear that citing Wong Kim Ark affirms Obama's NBC status rather than supports the notion that he is not a NBC.
Perhaps the author of your link has misused, or misunderstood Wong Kim Ark when she concludes that In all these quotes, two things are of importance: the use of the word Parents – plural meaning more than one, and the concept that the citizenship conditions of children follow from that of their parents. These historical references are clear in their meaning. In order to be a Natural Born Citizen, one must have parents - two parents, that are citizens of the Nation, and must be born on the soil of the Nation. It does not get any simpler than this..