Problem with that logic is that there really aren't any gaps left in the "natural born citizen" clause that Title 8 fills in. Title 8 may define classes of persons who are citizens at birth, but citizens at birth are merely a subclass of "natural born citizens," as that latter term was defined by Vattel and understood by the framers of the Constitution.
Since the Constitution was written and ratified, there is no case law which has changed the definition of "Natural Born Citizen" as it appears in Article II.
Thanks justiceseeker93.
Pardon my foggy brain, but don't you mean that "natural born citizens" are a subset (a special case) of all people who are "citizens at birth"?