US law s not affected by what Canada does or does not recognize. From 1968-1972 I went to college in upstate NY, and I had a number of classmates who had US and Canadian citizenship through the operation of different laws. When they turned 18, they had to choose.
I suspect that this was the situation with Cruz - he was a natural born Canadian AND a US citizen from birth, the former under Canadian law, the latter under US law. Because he moved to the US as a child, and in the absence of a military draft, there was never a need to clarify the situation.
None of this has been verified in a court. So we have all kinds of opinions about what Cruz is. The democrats will eat Cruz alive if he gets nominated.