The question with Cruz puts him even farther beyond NBC, as Cruz is admittedly a dual citizen at birth, born abroad.
That opens Pandora's box -- as if it wasn't opened already, by derelict Congress and chicken-scheist SCOTUS. Congress can't have the power to "make natural," both for reasons of simple logic (an Act of Congress can't change a boy into a girl, a person is born one or the other), and for reasons of preserving the nation. A rogue Congress could pass an Act that says either "all persons born in Iraq are citizens at birth of the US," or even simpler, "all persons born in Iraq shall be considered to be born in the US and subject to the jurisdiction thereof" The second form, if allowed, bypasses naturalization altogether, because the 14th amendment attaches citizenship on "born in the US" in combination with "and subject to the jurisdiction thereof." The first form looks like naturalization.
Congress always has a role - it counts the electoral ballots and has the power and duty to ascertain that the president-elect is qualified. Usually this is not contentious. But when it is, Congress has an amazing ability to clam up.
From my point of view, Congress and SCOTUS are subversive of the constitution.
I think the country is lost anyway, except as a name for a location on the planet. The people are lazy, sheepish, and gullible. I watch things unfold for entertainment.
I thoroughly agree with the last three paragraphs. Also, anyone born here or born to an American citizen is a citizen and subject to the laws of the US. If residing abroad, that person would also be subject to his/her country of residence. The exception as to those born here is that children born to foreign diplomatic personnel are immune from US jurisdiction. IIRC, if a foreign diplomat robs a bank here, we can turn him over to his embassy and demand that he be removed from the US by his nation of citizenship. If an ordinary non-diplomatic foreigner robs an American bank, he will not be an American citizen but he will be subjected to our laws.
Dual citizenship is not a simple concept for many Americans. The late actress Elizabeth Taylor was British by birth, American by naturalization and also an Israeli citizen who converted to Judaism and became also Israeli after marrying Eddie Fisher. I believe she held all three citizenships until her death.
Assuming that Congress may determine the electoral count and the qualifications of the president-elect, one other question remains: Does an action seeking a mandamus lie in such cases? That will depend on whether Congress's authority is discretionary or ministerial. If ministerial (mandatory outcome), mandamus lies. If not ministerial, courts can order the exercise of discretion but not dictate the specific choice to be made. That was, at least, the common law of Connecticut when I practiced there and obtained several writs of mandamus and I cannot imagine why the feds would have different standards..