There was not much Internet activity during the 1880s. Chester managed to mislead people by withholding his Vermont birth certificate, which was never found. That aroused enough suspicion, along with his journalist friend's book, that no one thought to examine Arthur's father's citizenship. Concealing with the intent of burning his fathers naturalization papers, no one bothered to Google William's naturalization docuemts. Chester served until his health prevented him from running for a term of his own, having become president when James Garfield was assassinated.
No one until the issue arose around Obama's legitimacy asked questions about Chester's father until Leo Donofrio, who had learned not to trust Internet documents and sought paper in libraries, or in the case of Chester Arthur, among the archives gathered by a Chester Arthur biographer. There was no mention in newspapers of the time and the Hinman book seems carefully to avoid the issue of Arthur's father's citizenship, which lends credence to the intentional misdirection hypothesis. In a book about presidential ineligibility, written just five years after the passage of Minor v. Happersett, there was no doubt about the need to have had parents who were citizens at the birth of the child.
I sincerely thank you for turning up the "Sun Yat-Sen Biographer" documents on Scribd. You may have noticed that the William Arthur birth certificate was provided by Sun Yat-Sen Biographer on 22 Jan 2009, just about the time Mr. Donofrio and his sister, whom I understand is an historian, discovered the document pictured at Scribd. You must have noticed that also provided at the Sun Yat-Sen Briographer Scribd locaton was the birth certificate of Sun Yat-Sen, the father of twentieth century China, born, according to the certificate of birth, in Honolulu in 1870. I had not seen the Hinman book, but can see why it was effective as misdirection.
It "sunyatsenbiographer" may not be Donofrio, who always dismissed the birth certificate issue as misdirection, but was certainly someone closely following his work since the media were in full see no evil, hear no evil, and write no evil about Obama mode in early 2009.
Of course in 1880, if anyone had cared about William Arthur’s citizenship status, they could have checked at the Hall of Records in Fort Edward, Washington County seat, New York.
In the Nineteenth Century, no one cared.