Trump and others denied that Obama was in fact born in the United States, but really, that is beside the point. Both men were born to American citizens, and it is reasonable to think that the child assumes the status of the mother. It sure did when a child was born to a slave woman. In a country where the rights of the mother over the child are paramount, where the American citizenship of the Mother was never given up, I conclude that Cruz is eligible.
There seems to be more to it when the requirement is “natural born citizen”, not a citizen in a general sense.