US Law.
Naturalization is a separate process.
See the US State Department’s Foreign Affairs Manual quoted below:
7 FAM 1131.6-3 Not Citizens by “Naturalization”
(CT:CON-349; 12-13-2010)
Section 201(g) NA and section 301(g) INA (8 U.S.C. 1401(g)) (formerly section 301(a)(7) INA) both specify that naturalization is “the conferring of nationality of a state upon a person after birth.” Clearly, then, Americans who acquired their citizenship by birth abroad to U.S. citizens are not considered naturalized citizens under either act.
How old was Cruz mother when she gave birth? How long did she live in the United States? Did she meet the requirements AT THE TIME to confer citizenship to a baby born on foreign territory to a non-citizen daddy?
That’s the evidence needed based on US Law which MAY have been applicable at the time.
Actually, that FAM text was updated today.
7 FAM 1131.6-3 Not Citizens by “Naturalization”
(CT:CON-479; 08-19-2013)
Section 101(a)(23) INA (8 U.S.C. 1101(a)(23)) provides that the term “naturalization” means “the conferring of nationality of a state upon a person after birth, by any means whatsoever.” Persons who acquire U.S. citizenship at birth by birth abroad to a U.S. citizen parent or parents who meet the applicable statutory transmission requirements are not considered citizens by naturalization.