The "Buffalo town" mentioned in some versions of the song must be in some other state, not Arkansas. The narrator says he was born in Buffalo and then traveled to Arkansas.

The Getty Thesaurus of Geographic Names—the most complete database I have found—lists 38 places named Buffalo, and a further 76 places formerly named Buffalo, or having a longer name that includes "Buffalo", e.g. Buffalo Bend, Buffalo Bluff, Buffalo Center, etc.