Wrong.
You’ve cited US Code which “grants” citizenship based upon certain circumstances.
Natural born citizenship is not gained through any sort of codification, it is “natural” by definition, and requires no law for it to be attained.
I really wish that you were correct, but you’re not. The Constitution is codified law (written in articles and sections).
“Birthright Citizenship In the United States:”
http://en.wikipedia.org/wiki/Birthright_citizenship_in_the_United_States
Besides, the Supreme Court ruled in 1874 that: “The Constitution does not, in words, say who shall be natural-born citizens. Resort must be had elsewhere to ascertain that.”—Minor v. Happersett