[Non-Sequitur]

This refutes the argument of those who maintain that Vattel doesn’t amount to anything. It is woven into SCOTUS precedent.

No, it's not. Three of those cases do not deal with the question of natural-born citizenship and the fourth doesn't say what the author thinks it says.

[Beckwith]

Sure they do — all FIVE of them:

http://www.theobamafile.com/ObamaNaturalBorn.htm#FiveCases