"seems unlikely to me that Shay and Berger would have taken this from Benet and changed the song. Benet is the literary person here. I would think that it is more likely that he adapted it."

Unlikely? Why? Simple and easy, especially if they assumed, as one might like to, that Benet had inside information. There's no basis for that assumption. What's more, the captain in Benet's poem really is named "Captain Ball."

Without a stated traditional source, there's no basis for accepting Benet's verse (or anyone else's) as traditional in any way.