Why? He served as president, it was public knowledge that his father was a British subject at his birth, and yet no one challanged his eligibility on that basis. That seems to be the perfect precedent for Obama's case.
It's my understanding that Arthur's father naturalized before Arthur reached majority. By the time most people would know of Arthur, they likely would have known his father to be an American citizen and probably had no reason to think otherwise and thus would not be likely to question his eligibility on the basis of his father's citizenship. Being born in Canada, however, would be a different story. Obama's papa, in contrast, never became an American citizen.