The U.S. Supreme Court has "clearly, unambiguously made the distinction between natural-born and a naturalized citizen, Elliott argued."No they didn't," [the judge] Pellegrini replied. ...
In the end, Elliott lost his case. Later in the day, Pellegrini issued an order leaving Cruz on the ballot, finding legal and statutory history that shows that a "natural born citizen" includes any person who is a U.S. citizen from birth.
Interesting that the judge finds "naturalized" and "natural born" to not be mutually exclusive.
A person born out of the jurisdiction of the United States can only become a citizen by being naturalized, either by treaty, as in the case of the annexation of foreign territory; or by authority of Congress, exercised either by declaring certain classes of persons to be citizens, as in the enactments conferring citizenship upon foreign-born children of citizens, or by enabling foreigners individually to become citizens by proceedings in the judicial tribunals, as in the ordinary provisions of the naturalization acts.
So Cruz was made a citizen by the authority of Congress, not thru naturalization. I would be surprised if Cruz lost.