Lets follow that logic to it’s natural end which is USC Title 8 Section 1401 subsection G which says that Sen Cruz is a citizen at birth and has not been nor never needed naturalization.
8 U.S.C. 1101(a)(23); INA 101(a)(23))
“Automatic” acquisition of U.S. citizenship after birth, a form of naturalization by certain children born abroad to U.S. citizen parents or children adopted abroad by U.S. citizen parents.
The only citizenship that can be conveyed to children born abroad to citizen parents is the citizenship conveyed by the 14th Amendment which is not Natural Born citizenship. That is available to their descendants who are born to 2 citizen parents.
7 FAM 1131.6-1 Status Generally
(CT:CON-636; 02-24-2016)
Persons born abroad who acquire U.S. citizenship at birth by statute generally have the same rights and are subject to the same obligations as citizens born in the United States who acquire citizenship pursuant to the 14th Amendment to the Constitution.