I think he is a natural born citizen. He is because the law says he is. He is because the Constitution gives Congress the authority to make all necessary law in that area. As you can see from the following US Code, Cruz was automatically a US citizen at birth, that is, a natural born citizen under the law. As this article says, every constitutional scholar consulted says he is.
So, the confusion appears to be that most folks don’t consider the last line in Article 1, Section 8. “To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof. “
Sec. 320. [8 U.S.C. 1431] (a) A child born outside of the United States automatically becomes a citizen of the United States when all of the following conditions have been fulfilled:
(1) At least one parent of the child is a citizen of the United States, whether by birth or naturalization.
(2) The child is under the age of eighteen years.
(3) The child is residing in the United States in the legal and physical custody of the citizen parent pursuant to a lawful admission for permanent residence.
OK, so he’s a citizen.
Next.