Sorry, you are confused on NBC because you are not paying attention to Article I Section 8 of the Constitution.
Congress is specifically enumerated with the power over all rules of naturalization. That includes who does and who does not need to be naturalized. A person who is a citizen at birth, who does not need to be naturalized, is naturally born a citizen and qualifies for NBC status.
Who is a citizen at birth is expressed in Title 8 section 1401. That includes all who are born on US soil (jus soli) per the 14th Amendment and is covered by sub section A. It also includes those born to a US citizen while abroad if they meet certain requirements and is covered by sub section G. This is the section that qualifies Sen Cruz.
You're are correct with regards to Congress having the enumerated powers with regards to the naturalization process. Which is quite different from being regarded as a "natural born" citizen. Naturalization can take place either by an immigrant coming here and going through a process to obtain citizenship, but it also can be bestowed upon persons at birth. A "natural born" citizen needs no confirmation that their allegiance is limited to the United States and the United Sates alone. That would be a person born within the territorial confines of the United States to citizen parents (plural).
In addition to the Constitutional requirements stating only a "natural born" citizen who has obtained the age of 35 is qualified to become President of the United States, the following must also be taken into consideration when determining "natural born" citizenship.
The United States vs. Wong Kim Ark.: "A person born out of the jurisdiction of the United States can only become a citizen by being naturalized...."
U.S. Department of State Foreign Affairs Manual: "Automatic" acquisition of U.S. citizenship after birth, a form of naturalization by certain children born abroad to U.S. citizen parents or children adopted abroad by U.S. citizen parents.
Ted was born abroad but to only 1 citizen parent. However, even if both had been citizen parents, he would still be considered a naturalized citizen
Cruz was a citizen at birth (jus soils) of Canada. He was a dual national until 20 months ago when he renounced his Canadian citizenship.
There is no doubt that Cruz is a US citizen. The question is whether he is a natural born citizen as it pertains to eligibility to be President under the Constitution. It is not settled law. It needs to be litigated.
