"I think Brian Peters does the song followed by the tune so I guess the two are incompatible."

They are compatible in the sense that they're both in 6/8, so it was a fairly obvious idea to use the tune as an interlude between verses of the song and see if anyone got the joke.

A lot of our well-known traditional dance tunes started out as songs in 18th century ballad operas and other stage productions, so it's possible the mysterious lines represent an old song that later got used as a dance tune. They do scan quite well to it.