Don't trust me, read the case yourself. Rogers v. Bellei, 401 U.S. 815 (1971)
Mr. Bellei was a US citizen who was born in Italy. His mother was a US citizen, his father was Italian.
Mr. Cruz and Mr. Bellei have identical birth circumstance for purposes of analysis, although Mr. Bellie's father never resided in the US - totally irrelevant factoid, but it is a potential difference in a different case.
Citizenship granted to Mr. Cruz and Mr. Bellei arises under slightly different statutes. As noted in opening, Mr. Bellei was a US citizen, as is Mr. Cruz. Under the Act of Congress that applied to Bellei, he had to reside in the US for certain number of years before he reached a certain age. It was a further condition, to maintain the US citizenship that he obtained at birth.
Mr. Bellei did not satisfy the conditions enumerated in the act of Congress, which created the issue that lead to the case. Mr. Bellei lost his citizenship, and sued to get it back.
If Bellei had been an NBC, his citizenship would not be subject to an Act of Congress, and could not have been stripped. The case would not exist.
The case was decided 5-4, turning on the meaning of "in", in the 14th amendment phrase "born or naturalized in the United States." Obviously, Bellei was not born in the US.
The majority said that Bellei was naturalized in Italy, not in the US. And so, it was not unconstitutional to strip him of his citizenship. The dissent felt this literal reading was wring, and "in the United states" should be read as "anywhere in the world."
The case is loaded with historical reference and at one point literally says "Bellei, as a naturalized American ..."
Don't take my word for it. I linked the case above. Correct me where I am wrong, or admit this is the was SCOTUS views citizenship acquired solely by operation of an Act of Congress.
"...Afroyim's broad interpretation of the scope of the Citizenship Clause finds ample support in the language and history of the Fourteenth Amendment. Bellei was not "born . . . in the United States," but he was, constitutionally speaking, "naturalized in the United States." Although those Americans who acquire their citizenship under statutes conferring citizenship on the foreign-born children of citizens are not popularly thought of as naturalized citizens, the use of the word "naturalize" in this way has a considerable constitutional history. Congress is empowered by the Constitution to "establish an uniform Rule of Naturalization," Art. I, § 8. Anyone acquiring citizenship solely under the exercise of this power is, constitutionally speaking, a naturalized citizen
Also:
The Fourteenth Amendment of the Constitution . . . contemplates two sources of citizenship, and two only: birth and naturalization. Citizenship by naturalization can only be acquired by naturalization under the authority and in the forms of law. But citizenship by birth is established by the mere fact of birth under the circumstances defined in the Constitution. Every person born in the United States, and subject to the jurisdiction thereof becomes at once a citizen of the United States, and needs no naturalization. A person born out of the jurisdiction of the United States can only become a citizen by being naturalized, either by treaty, as in the case of the annexation of foreign territory; or by authority of Congress, exercised either by declaring certain classes of persons to be citizens, as in the enactments conferring citizenship upon foreign-born children of citizens, or by enabling foreigners individually to become citizens by proceedings in the judicial tribunals, as in the ordinary provisions of the naturalization acts."