“Can you provide a link to where it was legally determined that Chester A. Arthur, or John McCain or George Romney weren’t eligible to be President?”
Chester A Arthur hid the evidence of his ineligibility...proof that he knew he wasn’t eligible. It was never adjudicated, and no other cases have been adjudicated either. But you knew that so your question is merely rhetorical.
Neither of the other two were ever elected to the Presidency so the question is moot.
I would say, however, that McCain, born to 2 American citizen parents serving their country in a US owned Panama Canal Zone (As a US Nava; Officer) would be judged a Natural Born Citizen, based on the perception that US Soil lies beneath the boots of every US serviceman on his assigned station. The Senate, in examining McCain’s eligibility, said the same thing in a “Sense of the Senate” Statement.
“The U.S. recognizes two kinds of citizens — an (sic) two only: citizen at birth and naturalized citizen.”
A Natural Born Citizen IS a Born Citizen. NBC describes a specific QUALITY of some (most, but not all) Born Citizens.
While all Natural Born Citizens are Born Citizens, not all Born Citizens are Natural Born Citizens See USSC Wong Decision, and read the 14th Amendment.
Of the many ways you can be considered a Born Citizen, only those born “...in a country to parents who are it’s citizens,” are Natural Born Citizens. Like I said it’s a QUALITY of certain Born Citizenships.
Alas, there is no definition of same in any law or legal proceeding. The Constitution expressly leaves the definition of citizenship to the Congress -- which defined the two categories of "born citizen" and "naturalized citizen" in a 1790 law. At th time, many of the founders sat in Congress and unanimously approved the law.
But you knew that, too, didn't you?
U.S. law doesn't subscribe to Vattel, it follows British Common Law.