Ted Cruz isn't a NBC of Canada because Canada says so, Ted Cruz is a NBC of Canada because he was born in Canada. period.
The supreme law of the US is the US Constitution. Not not English common law, not Canadian law, not any other law, dictionary or other material. Therefore it is irrelevant to the discussion.
So starting with the US Constitution, Article I Section 8 specifically enumerates Congress and only Congress with the power over the rules of naturalization. That includes ALL rules. Who is a citizen, who can become a citizen, who is a citizen at birth (naturally born a citizen).
Congress, through a series of acts starting with the naturalization act of 1790 through to current law, has expressed it’s will under the authority as detailed in Article I Section 8. In addition to the various amendments that impact the law (14th amendment for example), Congress’s authority with regards who is born a citizen and does not need naturalization, is expressed in Title 8 Section 1401.