The "country" surely didn't care about C.A. when he was a 14 y.o. and what citizenship status his father had when he was born. The issue, apparently, never came up. Why? I would venture a guess that nobody had a reason to doubt his eligibility when he was elected Vice President. The information wasn't widely known then, as it is more so now. It doesn't appear that he went public in a book (etc) saying that when he was born, his father was a foreigner. Furthermore, the "media" back then was far different than it is today, not having "thrill's" up their leg & actively cheerleading for the guy. C.A. had his papers burned upon his death. Gee, I wonder why? Something to hide perhaps?
No, Arthur didn't go public in a book, but...
The principal advocate of the “born in Canada” theory was Arthur’s fellow New York lawyer Arthur P. Hinman who was hired in 1880 by the Democratic Party to investigate Arthur’s ancestry. Hinman initially undermined his owned credibility by embracing an argument that Arthur was himself born in Ireland and didn’t come to the United States until he was fourteen years old. That story was patently false and easily disproven.
However, Hinman later discovered acquaintances of the Arthur family in Canada who told him the story of Arthur’s accidental Canadian birth. Convinced that he now had proof of Arthur’s foreign citizenship, he published his findings in 1884 in a short book entitled How a Subject of the British Empire Became President of the United States. Hinman’s book appeared near the end of Arthur’s presidency, and no official action was ever taken on the basic of his alleged evidence.
http://law.marquette.edu/facultyblog/2009/10/14/president-chester-a-arthur-and-the-birthers-1880%E2%80%99s-style/