I think you may be confusing citizenship itself with certification of citizenship. The consulate did not grant citizenship to those children, it merely provided documents they can use to prove the citizenship they were born with.
I'm not confused on that distinction. The grant of US citizenship to a person born out of the US comes from a statute. If the statute didn't exist, the consulate would not have the authority or a legal basis to issue a paper that documents the US citizenship of the child.