You cant say citizen=natural born citizen by what youve cited. Well, you could, but youd be wrong of course.
If there was no dispute over what a citizen is then that statute would say 'Natural Born Citizen' instead of the general term 'Citizen'.
You can't do nothing about that.
"THE VENUS, 12 U.S. (8 Cranch) 253, 289 (1814) (Marshall, C.J. concurring) (cites Vattels definition of Natural Born Citizen);
SHANKS V. DUPONT, 28 U.S. 242, 245 (1830) (same definition without citing Vattel)
MINOR V. HAPPERSETT, 88 U.S.162,167-168 ( 1875) (same definition without citing Vattel);
EX PARTE REYNOLDS, 1879, 5 Dill., 394, 402 (same definition and cites Vattel):
UNITED STATES V WARD, 42 F.320 (C.C.S.D. Cal. 1890) (same definition and cites Vattel.)"