Incorrect.
A person’s birth circumstances can not change, thus their citizenship is fixed at birth. Naturalization changes that status after birth via a legal process. That is why Title 8 Section 1101 subsection A part (23) (https://www.law.cornell.edu/uscode/text/8/1101) defines naturalization as:
The term “naturalization” means the conferring of nationality of a state upon a person after birth, by any means whatsoever.
Sen Cruz was born a US Citizen, has always been a citizen, has never needed to be naturalized and has never been naturalized. See USC Title 8 Section 1401 - Nationals and Citizens of the United States at birth. https://www.law.cornell.edu/uscode/text/8/1401
You keep making the assertions in defiance of the historical fact the U.S. Supreme Court decided such children acquired no U.S. citizenship after 1802 and until the naturalization acts once again gave them naturalized citizenship. You are also denying the fact many children born abroad with a U.S. citizen parent never become U.S. citizens.