A couple of thoughts.

In those days, "copyright" -- the idea that the creator of the work had any
kind of exclusive right to use and benefit from it -- was a very loose
concept and only a few radicals (like Twain) appear to have taken it very
seriously.

More important, I think it was important for Twain's comic purpose that the
jingle should appear to have simply appeared, like a force of nature, and
taken over the lives of those unfortunate enough to come in contact with it.
Attaching another writer's name to it would have complicated things.

Which, come to think of it, somewhat undercuts Twain's professed belief in
authors' rights, doesn't it?  But that's our Mark!

Pete Salwen