A child born to American parents outside of U.S. territory may be a citizen the moment he is born — but only by “naturalization,” i.e., by laws passed by Congress. If Congress has to write a law to make you a citizen, you’re not “natural born.”
Because Cruz’s citizenship comes from the law, not the Constitution, as late as 1934, he would not have had “any conceivable claim to United States citizenship. For more than a century and a half, no statute was of assistance. Maternal citizenship afforded no benefit” — as the Supreme Court put it in Rogers v. Bellei (1971).
That would make no sense if Cruz were a “natural born citizen” under the Constitution. But as the Bellei Court said: “Persons not born in the United States acquire citizenship by birth only as provided by Acts of Congress.” (There’s an exception for the children of ambassadors, but Cruz wasn’t that.)
So Cruz was born a citizen — under our naturalization laws — but is not a “natural born citizen” — under our Constitution.