Well, after listening to Hank Garland's recording of "Sugarfoot Rag," I'd say it's the same tune - but "Sugarfoot Rag" is an expansion of the tune for "Widder," so I'd say the copyright on "Sugarfoot Rag" is legitimate (and your implication that "Rag" is in the public domain is "iffy.") It sounds like you have pretty good documentation that the tune for "Widder" came from before 1923; so "Widder" is clearly in public domain, but not "Rag." I see nothing in general about the video that is a violation of copyright - but your implication that "Rag" is public domain, is problematic. So, yeah, I think I'd alter the video and re-post.
Say, I don't see the lyrics to "Pretty Little Widow" here at Mudcat. Can I talk you into posting them, Ritchie?

-Joe-