"What exactly is going on here?" Well, it seems that the audience is taking the name of the song less literally than the band is!

"Dueling Banjos" is just the name of a song. I mean, you don't need to be standing in a forest to play "Wildwood Flower", right? You don't need to have a cardinal perched on your shoulder to play "Red Wing." You don't need to fly yourselves and your audience to the US to play "Banks of the Ohio". So why not just play the song with the instruments at hand, and have fun with it? :^)