Now I am not going to claim this narrative as a fact, however it is a possible scenario. We know very well the history of Chicago's gang culture and we know the involvement of Al Capone in the rum running in the 1920's.

If these Chicago men had any relation to the rum running era which is very possible, it is very likely they heard the song in Nassau in the 1920's went back and copyrighted it.

I can't prove this but this is a possible scenario if they weren't aware of the Prouty version.