You are right of course, where he describes the songs origins as "a theory" - far from Jack's 'invention'
Elsewhere on the wed is is suggested it dates back as far as II76
I don;'t know th truth of this song but I do know Bert has been long enough dead to have the good manners not to accusing him of making anything up.
It becomes a little tiresome to see the reputation of people who gave us so much pleasure and inspiration exhumed and be administered a kicking when they are no longer around to answer for themselves
Nobody knows when these songs originated and we're all entitled to our theories
Jim