Wrong. If the child is born of an American citizen, even if they are born in Samoa, they are a citizen.
I welcome your citation. I posted mine.
Going back, to her great grandfather..
Benjamin Harrison Gabbard, Sr (1889-1932).
Benjamin came to American Samoa as a naval seaman in the late 19 teens and met and married Caroline Bartley of Western Samoa. He died in 1932 and is buried in the Satala Cemetery in American Samoa. Born in Boonesville, Jackson County, KY
https://www.findagrave.com/memorial/67421070/benjamin-harrison-gabbard