Unfortunately the courts have not agreed with that. In today’s world, anyone who qualifies under federal statutes as a Citizen of the United States At Birth seems also to qualify as a Natural Born Citizen, based on actual court rulings.
There is no example of a person who qualified as a Citizen of the United States at birth who was denied Article II Section 1 status as a natural born citizen, eligible for the presidency.
In 1884 the Supreme Court ruled in Elk v Wilkins, 112 U. S. 94:
“The distinction between citizenship by birth and citizenship by naturalization is clearly marked in the provisions of the constitution, by which no person, except a natural-born citizen, or a citizen of the United States at the time of the adoption of this constitution, shall be eligible to the office of president; and the congress shall have power to establish an uniform rule of naturalization. Const. art. 2, § 1; art. 1, § 8.
This section [of the 14th Amendment] contemplates two sources of citizenship, and two sources only: birth and naturalization. The persons declared to be citizens are all persons born or naturalized in the United States, and subject to the jurisdiction thereof.
-----------------------------------
Sorry, no. If "born a citizen" equals "natural born citizen," the Constitutional Convention wouldn't have rejected Hamilton's "born a citizen" terminology for Presidential eligibility. But they did.
“Unfortunately the courts have not agreed with that.”
Funny thing is...what the “court” decides is directly subject to the liberal/conservative majority of the Court. Therefore, what “The Court” has or has not agreed with, is irrelevant to what the Constitution actually states.
But, nice try.