I answered a different question earlier. The question you are asking pertains to Cruz.
The legal support, that Bellei is a naturalized citizen, is a premise (has no bearing on the decision of the case, just that case only arises because Bellei was naturalized) in the case of Rogers v. Bellei, 401 U.S. 815 (1971)
The case looks at the constitution, 14th amendment, and the Act of Congress that made Bellei a citizen of the US at birth, with no naturalization ceremony.
Thank you. That case is quite helpful, if not fully dispositive.