I agree that Congress has such authority. SCOTUS has not, however, issued an opinion on the matter of those born abroad to citizen parents.
The Act also establishes the United States citizenship of certain children of citizens, born abroad, without the need for naturalization: "the children of citizens of the United States that may be born beyond Sea, or out of the limits of the United States, shall be considered as natural born Citizens".
Since the Constitution gave Congress the authority to make that ruling, where is the issue?
They have not issued an opinion; however:
The Supreme Court has long recognized that two particularly useful sources in understanding constitutional terms are British common law3Ã
Both confirm that the original meaning of the phrase ânatural born Citizenâ includes persons born abroad who are citizens from birth based on the citizenship of a parent.
Used in Smitgh vs Alabama and other cases.