If you care to back and reinterpret Vattels conversation with himself, he looks at natural born from two perspectives.
1st he illustrates what he recommends because that is the Swiss view.
He then illustrates what other countries are doing, which I believe if what the framers adopted. So if you are dead set about using Vattel as a source, you need to use both positions that he mistakenly or intentionally mixes in the same chapter.
But whatever...
You are beating a dead horse. any suit will die as all the others have against Obama, and already one against Cruz. I seriously doubt that SCOTUS will EVER rule on this. Not enough people are affected and it has been applied in the way I explained it.
Other than Lawrence Tribe, a moonbat lefty and the moonbat press and a few bloggers, this issue had gone away. It will go away again. So, that's enough of this... Exit stage right.
It is an established maxim that birth is a criterion of allegiance. Birth however derives its force sometimes from place and sometimes from parentage, but in general place is the most certain criterion; it is what applies in the United States; it will therefore be unnecessary to investigate any other.
James Madison
Place. i.e. Jus Soli, native, Born in the USA and not in Canada