Your statement and those cases is irrelevent to the point I have made - that ‘natural-born citizen’ and ‘citizen at birth’ are one and the same. None of the Insular Cases rulings contradicted that basic point and in fact none made this claim - “individuals born there to legal residents are citizens, but not natural-born”.
A cite to back this spurious claim is welcome.
It’s Gabriel Chin’s argument and a sound one, WOSG.