No.Supreme Court precedent: The courts have applied the partus sequitur patrem principle (citizenship by descent from one’s father) to determine who is, or who is not, a federal (U.S.) citizen at birth; but the meaning of natural born citizen appears to be a separate issue [21]. To this day, the Supreme Court, in its majority opinions, has consistently used the term “natural born citizen” only in reference to persons born on U.S. soil, to parents who are both U.S. citizens.
In Scott v. Sandford (1856), Justice Daniel’s concurring opinion characterized, as unexceptionable (beyond criticism or objection), the Vattelian Law of Nations view of citizenship, which includes:
“natural-born citizens are those born in the country of parents who are citizens” (Scott v. Sandford, 1856)
In Minor v. Happersett (1874), children born in the United States were divided into two groups: (a) U.S.-born children of U.S.-citizen parents, and (b) all other U.S.-born children, regardless of their parents’ citizenship. The Court used the term “natural born citizen” only in reference to members of the first group [22].
In Perkins v. Elg (1939), the Supreme Court referred to Marie Elizabeth Elg as a natural born citizen. She was born in the United States; her father was a U.S. citizen by naturalization, and her mother was a U.S. citizen by marriage [23].
In Kwock Jan Fat v. White (1920), the Supreme Court referred to Mr. Kwock as a natural born citizen. He was born in the United States; his father was a native-born U.S. citizen; and his mother was a U.S. citizen by marriage [24].
To this day, whenever an Opinion of the Supreme Court has referred to an individual as a “natural born citizen”, the individual was always born in the United States, of U.S.-citizen parents. The Supreme Court has never, in any of its majority opinions, used the term “natural born citizen” in reference to someone whose parents were not both U.S. citizens
All this means is that a child born on US soil to parents who are both citizens is unquestionably a natural born citizen. No one has ever disputed that.
Your point adds nothing to whether the founders intended “natural” to be jus soli or jus sanguinis or require both. The answer to that is clearly seen in the 1790 act.
Your point is pertinent in that the current Supreme Court, if it was willing to rule on the matter, would not be bound by any precedent.
My opinion is that the Supreme Court would rule that Cruz met the Constitutional criteria for president. And further, regardless of how they ruled, virtually no one would change his or her opinion on the matter. They would simply agree with the court or disagree.