By "the ballad traveled the world, Walker means the whole gamut based on "The Unfortunate Rake." I see nothing to relate it to the song considered in this thread, or even to "Rocking the Cradle."

Quoting Walker on "St. James Infirmary":
A story by Al Rose in his Storyville, New Orleans: "According to a common legend, the church (St. James Methodist) offered first-aid services and modest hospital facilities and thus became the inspiration for the widely performed St. James Infirmary Blues. Unfortunatey this colorful and imaginative legend is not true; indeed the song has no connection with New Orleans."
Walker does kill that legend, but unfortunately his story based on the Unfortunate Rake is speculation.

If you want a good intertwining of Unfortunate Rake with St James Infirmary, etc., get the Smithsonian cd on the Unfortunate Rake and read the insert. Some of it must be taken cun grana salis as well.