If anybody actually looked at the link I provided earlier, they'd see that all this has already been said.

Perhaps I had better mention, since there is obviously some confusion here, that 'Sweet Joan' in the DT is one of Stephen Sedley's eccentric collations. Under the mistaken impression that 'Crafty Maid' was a 'bawdy version' of 'Lovely Joan', he took a few lines from a broadside edition of the former, changed them a bit, and set them to a 'Lovely Joan' tune he had found in the Journal of the Folk-Song Society (vol I, issue 5, 1904, page 270, as it happens; though he didn't say so at the time) and compounded the error by giving the mutant result the wrong title.

In the circumstances it isn't surprising that this has confused people. It is a 'version' of 'Crafty Maid', technically; but not a traditional one. Nobody had ever sung it like that prior to Sedley's book (1967).