I agree that US laws govern his US citizenship and any other nation’s laws are irrelevant to his US citizenship. Thus US laws are exclusive to the US.
Each nation state governs it’s own laws of citizenship and as such, Canadian laws govern Canadian citizenship (again, exclusively).
Cruz was born in Canada. By Canadian law he is a natural born citizen of Canada.
US law are naturalization statutes.
Cuban laws.... ?
And apparently from your perspective, British law governs us both. What is a "British Common Law" advocate to do when two different countries follow the exact same Common law?
How is a third country supposed to figure out which British law has the better claim? Or is he up for grabs by anyone?