Some versions of 'William Taylor' are also the burlesque version.

Or a bit of both? The version Tony Rose recorded seems pretty straight but for the last verse ("If young people in Wells or London"), which is out of a burlesque.

I suspect sometimes a burlesque gets taken for an original because the humour wasn't broad or obvious enough for a new audience to spot. This need not be because the burlesque writer's sense of humour was tremendously subtle; it might just be that the burlesque wasn't that good, possibly because it was dashed off as a fairly close copy of an original ballad with a few gags or bits of bathos stuck in.