It should not figure at all. It was not publicly known that Arthur's father was not a citizen at the time of his birth, or until long after his passing for that matter. Just because someone else violated the Constitution and got away with it, without the issue making it to any court, let alone the Supreme court, is no legal precedent at all. One way or the other.
Since it was being publicly alleged that Chester Arthur himself was born in Ireland, it must have crossed more than a few minds that his father was still an Irish citizen.
“It was not publicly known that Arthur’s father was not a citizen at the time of his birth”
Actually it was known that Chester Arthur had a foreign father. Like Obama, Chester Arthur had an American mother and the official story was that he was born in the US (Vermont), and thus a natural-born citizen.
Attempts to suggest that Arthur wasnt born in Vermont but was born in Canada didnt make a difference - see:
http://en.wikipedia.org/wiki/Chester_A._Arthur
“During the 1880 U.S. presidential election a New York attorney, Arthur P. Hinman, was hired to explore rumors of Arthur’s foreign birth. Hinman alleged that Arthur was born in Ireland and did not come to the United States until he was fourteen years old. When that story failed to take root Hinman came forth with a new story that Arthur was born in Canada. This claim also fell on deaf ears”
History repeats itself.