But Blackstone's Commentaries was THE work on English common law. And Blackstone says that a child born in England was a natural born English subject regardless of the nationality of the parents. Don't cherry-pick Vattel and pretend that the whole world agreed with him on the subject.
Blackstones commentaries are talking about who is “subject to the king”, and says they are all who are born “in the dominion(s)”.
He is not talking about “natural born citizen” of the United States.