I read that his mother registered his birth at the US consulate in Canada. And that he needed a US passport in High School to travel on a class trip to England. What was not made clear is if the registration was when he was a tyke or a teen. As he is a statutory citizen it makes no difference in his citizenship here. I think this whole releasing his moms birth certificate is silly as no one questioned if he was a statutory citizen by virtue of her being a US citizen.
I read the same, that there is a CRBA and a passport. I don't doubt that Cruz has US citizenship, and I agree with you, it is citizenship derived by operation of a statute.
I don't think his mother's BC proves the case, without more. 1401(g), the relevant statute, requires her to be a citizen at the time of the child's birth (I think she was, but her BC isn't determinative of her citizenship status years later), and residency in the US (again, i think she has this, but her BC doesn't have evidence of residency). I also don't think showing her BC is necessary. Ted's BC says the same thing that his mother's BC establishes, that she was born in the US.
A CRBA would be conclusive (of citizenship), as it accounts for the relevant factors. A CRBA isn't necessary, because those factors can be demonstrated with other evidence. I think the other (anecdotal) evidence results in finding the conditions for 1401(g) citizenship are met.
I don't think Cruz is a natural born citizen, because his citizenship depends on a statute. He is not "naturally" a citizen, he is a citizen because Congress chose, as it is empowered to do, to grant citizenship to persons who would not be citizens by operation of natural law. Not that my opinion matters, others will decide the issue, and that decision will be based solely on the outcome the deciders prefer, with no regard to precedent.