I think you might be right about the CRBA.
Cruz has provided his Canadian Birth Certificate and his mother's Delaware birth certificate. This establishes his birth to a woman born in the U.S. At this point, we do not know if his mother is still a U.S. citizen or born in the U.S. This is important, because the CRBA requires proof of U.S. citizenship by at least one parent. We also know through news reports that Cruz' parents were eligible to vote in Canadian elections and were listed as Federal electors. So was Ted's mother a U.S. Citizen or Canadian citizen at that time?
Now here are the relevant parts of the CBRA instructions.
A child born abroad to a U.S. citizen parent or parents may acquire U.S. citizenship at birth if certain statutory requirements are met. Parents of a child born abroad to a U.S. citizen or citizens should apply for a CRBA and/or a U.S. passport for the child as soon as possible. Failure to promptly document a child who meets the statutory requirements for acquiring U.S. citizenship at birth may cause problems for the parents and the child when attempting to establish the child's U.S. citizenship and eligibility for the rights and benefits of U.S. citizenship, including entry into the United States. By law, U.S. citizens, including dual nationals, must use a U.S. passport to enter and leave the United States.
So for Cruz to establish his citizenship and to be living in the U.S. by law, he or his parents needed to apply for and have approved a CRBA and a U.S. passport. Cruz has thus far provided neither. So at the present time, beyond providing his mother's birth certificate, Cruz cannot even prove he is a U.S. citizen. The merits of his NBC status are irrelevant at this point. Cruz has his records sealed and this should concern everyone. Cruz has thus far advanced a legal position of his NBC status that he cannot at the present moment prove. I will note that the CRBA states that a child "may acquire citizenship at birth" which to me is a whole different category than NBC. If you were an NBC there would be no need to "acquire" citizenship.