Many of us make no such argument, rather only that Minor clearly supports the operative meaning of NBC at the time (i.e., the intent of the founders).
When the court said ...it is not necessary to solve these doubts... it was referring to the doubts purportedly raised by some regarding ordinary citizenship. these doubts does not refer to NBC, for which there were no doubts
The argument isn't misstated. That Minor was decisive is manifest from the fact that the Supreme Court unanimously rejected Virginia Minor's argument of being a citizen by virtue of the 14th amendment AND that the decision was cited decisively more than 20 years later in Wong Kim Ark, when the court noted that children born in the country of citizen parents were EXCLUDED from the citizenship clause of the 14th amendment and summarized Minor's citizenship as being a product of BOTH jus soli and jus sanguinis criteria:
That neither Mr. Justice Miller nor any of the justices who took part in the decision of The Slaughterhouse Cases understood the court to be committed to the view that all children born in the United States of citizens or subjects of foreign States were excluded from the operation of the first sentence of the Fourteenth Amendment is manifest from a unanimous judgment of the Court, delivered but two years later, while all those judges but Chief Justice Chase were still on the bench, in which Chief Justice Waite said: "Allegiance and protection are, in this connection" (that is, in relation to citizenship),
reciprocal obligations. The one is a compensation for the other: allegiance for protection, and protection for allegiance. . . . At common law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children, born in a country of [p680] parents who were its citizens, became themselves, upon their birth, citizens also. These were natives, or natural-born citizens, as distinguished from aliens or foreigners. Some authorities go further, and include as citizens children born within the jurisdiction, without reference to the citizenship of their parents. As to this class, there have been doubts, but never as to the first. For the purposes of this case, it is not necessary to solve these doubts. It is sufficient for everything we have now to consider that all children born of citizen parents within the jurisdiction are themselves citizens.
Minor v. Happersett (1874), 21 Wall. 162, 166-168. The decision in that case was that a woman born of citizen parents within the United States was a citizen of the United States, although not entitled to vote, the right to the elective franchise not being essential to citizenship.
Earlier in the WKA decision, Justice Gray reinforced this point by noting that the Constitution (after its 14th amendment was construed) did NOT say who NBCs are:
In Minor v. Happersett, Chief Justice Waite, when construing, in behalf of the court, the very provision of the Fourteenth Amendment now in question, said: "The Constitution does not, in words, say who shall be natural-born citizens. Resort must be had elsewhere to ascertain that." And he proceeded to resort to the common law as an aid in the construction of this provision.
Before anyone misreads the previous passage, Gray does NOT say common law is used to define NBCs. He said common law was used as an "aid" in the construction of the citizenship provision of the 14th amendment. Summarized: NBCs are not defined by the Constitution. NBCs are EXCLUDED from the birth clause in the 14th amendment. The birth clause of the 14th amendment is interpreted in the light of the common-law. The cited common law relies on parents adhering to the United States in their allegiance. This means if they aren't citizens, they must have an expressed intention to permanently reside in the U.S., which is established through permanent domicile.