Not a joke or a misprint. Bumbling around doing research for the Beowulf post, I happened across an essay by Guy Davenport, literature prof in KY who studied under Tolkien at Merton College, Oxford. Back in the US, he became friends with Alan Barnett, who he later learned had been a student at Oxford with Tolkien. Barnett related how fascinated JRRT had been to hear about the country folk of Kentucky, growing tobacco and having such English country names as Burrowes, Barefoot, Proudfoot, and Baggins. Two versions of the same story, each with information the other lacks, are here (scroll down) and here. Barnett, BTW, had not heard that his friend Tolkien had later become a novelist and knew nothing of The Lord Of The Rings.
Davenport wrote a NYT piece on it in 1979, but the Times archive only goes back to 1981.
Commentary. The rural West Midlands area that Tolkien patterned the Shire after had become more urban by the time of Tolkien's writing, and the idea of something even remotely like it being preserved in America might well have charmed him. To a European classicist, rural America had much the same remoteness that Professor T was trying to capture about the Shire. Americans would immediately associate Kentucky with Appalachia, which was settled by rambunctious Scots-Irish and English Borderers, and discount the idea of any connection. But Tolkien may not have had that association, and in this case it is not accurate anyway. That section of KY between Frankfort and Louisville was actually settled by a higher percentage of West Midlanders, more like Ohio was.
I looked up all those Hobbit-names, comparing that part of KY with the rest of KY, and with other places across the US. There weren't any Bagginses,* Gamgees, or Bracegirdles, but there were Tookes, Grubbs, Barefoots and Proudfoots, Burrowes, and Pippins. There were no Butterburs, but there were Butterbaughs. BOOderbaw my son pronounced immediately after I'd told him. "We had a Butterbaugh in my class (at Asbury College in Kentucky)" There was indeed a greater concentration of all these names around Shelbyville and Louisville. These names occurred elsewhere in the country, but were much less common - only a few in huge California, New York, and Texas, for example.
The attempts to show a similar speech pattern I find less convincing. Rural archaic constructions all sound very similar at first go until you take them apart. That archaic constructions persisted at all, however, would have been known to Tolkien but still likely to intrigue him.
One commenter on a Tolkien site suggested that examining the census records for 1910 - 1930 for that area might be more revealing than a current phone listing. Likely true, but I'm not likely to do it myself.
Update: There is a Cooter Baggins who graduated from a HS in Indiana, right across the river from that part of KY. Hmm.
*There is a Bilbo Baggins in Louisville, but I assumed that was a taken name, not a christened name.