Yes, however Blackstone is clearly describing English law and its development in particular and not inducing larger points of natural law. Those points after all, are deduced, as the other commentators imply. Natural law would not carry much weight (or none) with Justice Scalia, anyway.
Tucker and Bingham do an excellent job of spelling out contempraneous understanding of what "natural born Citizen" means/meant to the framers (birth both in state and by citizen father, hence Tucker's "hereditary right").
Clearly, from John Jay's request (instruction) this was a defensive measure. I.e., he wanted to plug potential allegiance holes! (Both of them.)
Pinging some ol' philosophy buffs FY-somethingerother.
Thanks for the ping!