“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.
It was known that the father was born in Ireland, but apparently it was not widely known at the time that the father was not a naturalized citizen of the US until long after Chester Arthur's birth.
It was known that his father was foreign born, lots of citizens were, but not that he was a foreign national.