“Cruz and my daughter became citizens of the United States by birth, not naturalization.”
No they did not. If your daughter was born abroad and outside the jurisdiction of the United States, meaning without diplomatic immunity, she could only acquire U.S. citizenship by naturalization at birth or naturalization after birth. Recently it was made an illegal act for a U.S. citizen to depart or to enter the United States without a valid U.S. passport. Previously, we used to be able to cross the Canadian-U.S. border with our U.S. state driver’s license. The U.S. Immigration and Naturalizations Acts require a Consular Report of Birth Abroad (CRBA) Form FS-240, Certification of Report of Birth Form DS-1350, or U.S. Citizenship and Immigration Services (USCIS) Certificate of Citizenship as the circumstances require to document the acquisition of U.S. citizenship by naturalization at birth and to obtain a U.S. passport.
Now I know you are full of it. My daughter was born in Singapore while I was posted as a US diplomat in Jakarta. Both my wife and I are US citizens. I personally filed a Consular Report of Birth and received the documentation to bring my daughter back to Jakarta. After that, my daughter was added to my wife's diplomatic passport for travel back to the US. Eventually, my daughter was issued a US passport. She was never naturalized. She never received a certificate of naturalization. She is a US citizen by birth (jus sanguinis), not thru naturalization.
Whether she is a NBC is another matter. I believe she is but the courts have never litigated the issue.