I think you are taking this tourist board narrative too far.

Tourist board would be a organization that look for promoters to bring people to the Bahamas. This doesn't mean the songs themselves haven't already existed and it doesn't mean American visitors didn't come to the islands hear the songs and take it back to their actively competitive culture in the USA which is full of copyrighting and publishing music a tradition which would not have been widespread if at all active in The Bahamas at the time.

The songs are Bahamian no one can argue that at all.