It can be argued that Cruz’s father threw off any allegiance he may have had by becoming a political refugee/exile. He fought against Batista but became disillusioned and expatriated himself. The Cuba in which he was born no longer existed as a political entity and the one that arose in its place can be said to have had no internationally recognized legal jurisdiction over the senior Cruz, therefore there exists the possibility that neither of Ted Cruz’s parents were under the jurisdiction of some other sovereignty.
Of course, that would still leave the matter of his being born in Canada to resolve. If Canada did not claim jurisdiction over Cruz as a result of his having been born there (some nations do, some nations don’t), and neither of his parents owed any allegiance to a foreign sovereignty, then I’d go so far as to say that he meets the requirements for eligibility.
If it is found, however, that the senior Cruz actually was under the jurisdiction of Cuba at the time of Ted Cruz’s birth, or Canada did claim him as a citizen at birth, then he does not meet the requirements.
Anyone who is claiming that determining natural born citizenship status, for anyone other than those born in the country to two citizen parents, is an easy thing to do, is mistaken. This is the unresolved area of doubt to which Chief Justice Waite referred in Minor v. Happersett. It clearly was not easily resolved then and still isn’t now, because so much depended upon individual circumstance and other claims of jurisdiction that cannot be consistent from one individual to the next.
Cruz’s mother, from what I have read, was a US citizen at the time of his birth. If his father had not officially renounced, (however one does that officially and legally) his Cuban citizenship, then he was a Cuban national. It hardly seems possible that he reamined “a man without a country” for decades, as he only naturalized as a US citizn in, I think, 2005.
And being born in Canada where his parents were living and continued to reside for 4 years, is also disqualifying.