You're living up to your moniker. No one said Vattel was the law of the land; just that the Supreme Court used his definition of natural born citizen.
If it was we'd have an official national religion.
For the blind faithers who religiously defend the undocumented occupant in the Oval Office, they already do.
Vattel is used in context like a legal dictionary that the framers used so we can understand the terms they used in the legal context they viewed them from. There may be terms we use now that had a different context or meaning when the framer's wrote the Constitution. It isn't an end, but it is a means to an end, it gives the NBC argument (re two citizen parents) a legal base to start from.
Not in a binding decision, no.