[T Ruth]

Thanks to your hint, I did some research. Although the history of the law is convoluted, it seems clear that in Cruz's case his citizenship was acquired by birth and not by naturalization.

Here is a pretty good discussion, U.S. Citizenship Acquired by Birth Abroad. It's a 2011 article by a Canadian lawyer. The date of the article implies to me that the lawyer had no axe to grind on this issue.

[Ray76]

Citizenship was acquired by statute.

See Rogers v Bellei