correct
and the phrase Citizen at Birth appears nowhere.
Naturalization as a basic “Citizen” kind of Citizen at birth is granted via U.S. man-made naturalization law Title 8 Section 1401 enacted under the naturalization powers granted to Congress in the U.S. Constitution: https://uscode.house.gov/view.xhtml?req=granuleid:USC-prelim-title8-section1401&num=0&edition=prelim