It’s worth keeping in mind that there are two types of citizens——naturalized and natural born.
Cruz has never been naturalized. There was no need.
Naturalized "at birth" by the Immigration and Nationality act of 1952.
His sort of case is listed under this heading in the act.
Title III-Nationality and Naturalization
Chapter 1-Nationality at Birth and By Collective Naturalization
"Collective Naturalization" refers to all those people who fit in the category designated in the act of having at least one American Parent.
It's under Title III of that act, but for some reason, every copy I find omits Title III. I found it years ago, because I quoted from it, but I am not finding it now. It simply jumps from Title II to Title IV.
Weird.
Oh, and look what I found here:
(3) an alien born in the United States shall be considered as having been born in the country of which he is a citizen or subject, or if he is not a citizen or subject of any country then in the last foreign country in which he had his residence as determined by the consular officer;
Seems as though that would apply to Obama and "Anchor Babies."