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.
you are making stuff up. The supreme court recognizes the common law as being the basis to understanding the constitution and the common law says a natural born citizen is someone born into allegiance of a particular sovereign holding dominion over the place of birth. Ted cruz was born into the allegiance of Canada and that makes him a NBC and that’s why the Canadian law defines him as a NBC. I can easily show you a dozen statements pulled out of supreme court opinions that support this reality.
If the will of Congress, expressed in a statute, was that children born in Cambodia, of Cambodian parents, are citizens of the US at birth (and it is ludicrous to think an infant is competent to participate in a naturalization ceremony), such an Act is valid under the power of Congress to naturalize. By your rule, these persons are NBC of the US. But your rule is not the one that operate in the law.
By the way, those hypothetical Cambodians would, as a matter of law, be citizens of the US.
We can look to the constitution, which contains the will of the founders. Art IV, Sec. 2 says that a person who is a citizen of a state is at the same time a citizen of the US. By your rule, Congress could change this, too, by Act of Congress.