As I recall, the argument on Ted Cruz' side is that a natural born citizen is one who is a citizen by virtue of the fact of birth rather than by virtue of adjudication. That principle, the argument goes, applies even though one fills out forms in a foreign country which simply automatically gain the baby citizenship.
This means that Congress has the power or the authority to define natural born citizen because the Constitution vested that authority in Congress, the phrase not being otherwise defined in the document and thus Congress is not superseding the Constitution. The first Congress seems to have assumed that was the case.
You believe that the next Congress disagreed and they well might have, even Scalia, however, would not presume to tell us which. On the other hand, the next Congress might simply have been redefining its notion of what qualified or should qualify for natural born citizenship.
I think there are strong arguments to the contrary, but as I say, the Cruz side is not without its arguments and has a procedural history indicating that it might never get litigated.
