>>>Clearly Cruz was naturalized at birth..
No, there is no such thing.
One is either born a citizen or goes through the process of naturalization. There are clear requirements for becoming a naturalized citizen:
https://www.uscis.gov/sites/default/files/USCIS/files/M-1051.pdf
https://www.uscis.gov/us-citizenship/citizenship-through-naturalization
Yes, born a citzen, thanks to Congress. But NOT A NATURAL BORN CITIZEN BY ANY MEASURE.