Malcolm, I wouldn't completely write off the theory that the song arrived in America with Irish immigrants. The difference might be that it was the Scotch-Irish in the 18th Century rather than the famine-era Irish who brought it. The Scotch-Irish largely came into America through Pennsylvania before moving down through the Valley of Virginia and points south and west. A lot of their music would have contained strong elements of the Scots and English traditions and it would not be stretching it to believe that a variation of The Water is Wide would come with them.