Proof and Truth are not something the tRumpster are good at, nor do they care about it. It is whatever they say it is.
The Proof is in the law that defines the Truth
1952 & 1965 Immigration & Nationality Acts that governed the status of Cruz's nationality at birth defined Raphael Edward Cruz as one who...
... entered the US at the age of 4 as a “non-quota” immigrant http://legislink.org/us/pl-82-414
Section 101 (a) (27) The term “nonquota immigrant” means— (A) an immigrant who is the child or the spouse of a citizen of the United States;
PROCEDUKE FOR GRANTING NONQUOTA STATUS OR PREFERENCE BY REASON OF RELATIONSHIP
SEC. 205. (a) In the case of any alien claiming in his application for an immigrant visa to be entitled to a nonquota immigrant status under section 101 (a) (27) (A), or to a quota immigrant status under section 203 (a) (2) or 203 (a) (3), or to a preference under section 203 (a) (4), the consular officer shall not grant such status or preference until he has been authorized to do so as provided in this section. (b) Any citizen of the United States claiming that any immigrant is his spouse or child and that such immigrant is entitled to a nonquota immigrant status under section 101 (a) (27) (A)
... so is “fair”.