This means that 14th amendment citizenship was not the question with Bellei. His citizenship was based on birth abroad to a US parent and that was under the purview of Congress, based on the authority given them in the US Constitution.
Our National Legislature indulged the foreign-born child with presumptive citizenship,
In the case of Bellei, who had refused to observe the requirements of the law for retaining his citizenship, the US stripped him of his citizenship. He wanted that ruled unconstitutional. The Supreme Court upheld the law that he could be stripped.
The italics above is simple recognition that in bloodline citizenship that Congress is empowered by the US Constitution to make what it considers to be reasonable law.
Therefore, the law it makes on this subject is binding.
The current law says the following are both nationals and citizens at birth (item (g) is the case of Ted Cruz):
INA: ACT 301 - NATIONALS AND CITIZENS OF THE UNITED STATES AT BIRTH
Sec. 301. [8 U.S.C. 1401] The following shall be nationals and citizens of the United States at birth:
(b) a person born in the United States to a member of an Indian, Eskimo, Aleutian, or other aboriginal tribe: Provided, That the granting of citizenship under this subsection shall not in any manner impair or otherwise affect the right of such person to tribal or other property;
(c) a person born outside of the United States and its outlying possessions of parents both of whom are citizens of the United States and one of whom has had a residence in the United States or one of its outlying possessions, prior to the birth of such person;
(d) a person born outside of the United States and its outlying possessions of parents one of whom is a citizen of the United States who has been physically present in the United States or one of its outlying possessions for a continuous period of one year prior to the birth of such person, and the other of whom is a national, but not a citizen of the United States;
(e) a person born in an outlying possession of the United States of parents one of whom is a citizen of the United States who has been physically present in the United States or one of its outlying possessions for a continuous period of one year at any time prior to the birth of such person;
(f) a person of unknown parentage found in the United States while under the age of five years, until shown, prior to his attaining the age of twenty-one years, not to have been born in the United States;
(g) a person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years, at least two of which were after attaining the age of fourteen years: Provided, That any periods of honorable service in the Armed Forces of the United States, or periods of employment with the United States Government or with an international organization as that term is defined in section 1 of the International Organizations Immunities Act (59 Stat. 669; 22 U.S.C. 288) by such citizen parent, or any periods during which such citizen parent is physically present abroad as the dependent unmarried son or daughter and a member of the household of a person (A) honorably serving with the Armed Forces of the United States, or (B) employed by the United States Government or an international organization as defined in section 1 of the International Organizations Immunities Act, may be included in order to satisfy the physical-presence requirement of this paragraph. This proviso shall be applicable to persons born on or after December 24, 1952, to the same extent as if it had become effective in its present form on that date; and
(h) a person born before noon (Eastern Standard Time) May 24, 1934, outside the limits and jurisdiction of the United States of an alien father and a mother who is a citizen of the United States who, prior to the birth of such person, had resided in the United States. 302 persons born in Puerto Rico on or after April 11, 1899
And you are suggesting that Congress has a higher authority than does the 14th amendment?
We already know from Minor v Happersett that the 14th amendment does not determine who shall be a "natural born citizen." Straight from Judge Waite's mouth.
The significance of Congressional authority over citizenship granted at birth to those born abroad is, according to the Rogers v. Bellei SCOTUS decision, that such citizenship is not a constitutional right, can be denied or revoked, and can be subject to certain requirements.
The same does not apply to 14th Amendment citizens who are born in the United States. Such persons have a guaranteed constitutional right to their citizenship and no action by Congress (absent a Constitutional amendment) can deny such citizenship, revoke it without a citizen's consent, or attach requirements to retain such citizenship.
That is a significant legal difference between a natural-born citizen under the 14th and a statutory natural-born citizen (citizen at birth) under the INA, don't you think?
For the sake of argument, assume that a citizen at birth (under the INA) is POTUS and Congress then passes retroactive changes to the INA that make that person a naturalized citizen instead of a citizen at birth. A mere legislative change by Congress can make the POTUS suddenly ineligible to hold the office to which he was elected. (Admittedly far-fetched, but you get the point, right?)