Rules of naturalization have nothing to do with rules governing natural born citizens, which is defined by the standards of natural law. For example, from the book "Laws of Nations" written in 1758:
"The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives, or natural-born citizens, are those born in the country, of parents who are citizens. As the society cannot exist and perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights."
From the point of view of the founding fathers, Ted Cruz would be Canadian, because he was born in Canada to a father of Canadian citizenship. He would not be a "natural born citizen."
Incorrect.
The rules of naturalization define who is a citizen at birth and as such, define those who are naturally born as US citizens.
The book “Laws of nations” has no authority under the US Constitution which is the supreme law of this nation. As such, only CONGRESS has the enumerated power to set the rules of who does and who does not need to be naturalized.
Further, the very first act of Congress, the Naturalization Act of 1790 set the precedence that being born on US soil is NOT a requirement for citizenship at birth.