Why should Chester Arthur not have been president? He was born on October 5, 1829, in North Fairfield, Vermont. To my knowledge Vermont is a US State
At the time of his birth one parent was not an American citizen. Also there was doubt that he himself was born in the US and not Canada.
As the Senate Resolution on McCain says"
Whereas the term "natural born Citizen", as that term appears in Article II, Section 1, is not defined in the Constitution of the United States;
The issue has never beem adjudicated.