Prove that he did do this and you're a long way toward resolving any doubt regarding the existence of internationally accepted claims of jurisdiction by Cuba upon children of the senior Cruz.
Everybody has been so caught up, looking for “the” definitive rule or law, when it's been reasonably clear from various courts that the answer is, it depends. There are doubts regarding certain circumstances of birth, however these doubts can be resolved, in the affirmative or in the negative. Birth circumstance varies widely from one individual to the next. A single law covering them all was not feasible.
Eligibility was clearly to be determined on a case by case basis, for those in a position of doubt. The only individuals for whom there was and is no doubt, are those born under the full jurisdiction of the United States, to citizen parents. There is no other avenue possible for a foreign jurisdiction to make any internationally recognized legal claim of jurisdiction upon such individuals. Others not born in this circumstance can be found to be free of foreign jurisdictional claims, but it just isn't clear cut.
Through his mother, there is not doubt of Ted Cruz’s US citizenship at birth.
My mentioning the father is hypothetical and is based on the ease with which it was possible to acquire citizenship on the old frontier...so far as the requirements are concerned. It was simply a number of years as a resident and then an oath before any magistrate anyplace at any time.
The difficulty had to do with any travel really. I’m sure many on the Kentucky County frontier considered themselves citizens but were prevented by the situation from traveling great distances.