No, they incompetently assumed Chester Arthur was born in Ireland or Canada. They were so intent upon trying to prove the fallacy, they failed to see the obvious in front of their noses.
Because the records were sealed for 70 years, the invesitgators did not have access to the naturalization records which would have disclosed the father’s naturalization after the son’s birth.
You say that the "records" were sealed for seven decades, and so investigators couldn't discover that Arthur's father was naturalized after his birth. If you please, answer me one question: Did they know that Arthur's father was born on Irish soil as an Irish subject? They didn't know about the post-birth naturalization, fine. But did they know that?