The Balfas don't sing exactly the same melody as Happy Fats (my favorite). I can't tell what notes they changed but their version is slightly different to my ears (sounds out of tune, in fact ) . I couldn't find Happy Fats' version on Internet but it is on this CD:
It's a kind of hocus-pocus and I couldn't believe it.
But there are parts in the songs that are similar.
It's not so obvious as in the Valse de Cherokee and the Midland Two Step.(for me)