I said, "known", not "speculated". I'm sure it did cross a few minds, but they were so intent on finding the "foreign birth certificate", or at least proof thereof, they didn't look for naturalization papers for his father. Of course since Arthur actively concealed the fact, missing only the copy in the National Archives, even if they had looked, they might not have found it.
There were really no "birth certificates" as we know them today in those days. Births, and marriages for that matter, were recorded in the family Bible, or equivalent, and in church records. Churches without infant baptism might not have a record of place of birth either.
Apparently historians are agreed that the issue of Arthur's birthplace has been set to rest by the discovery of the Arthur family Bible. If there were such a thing as the Obama family Bible, I don't think it would suffice.