Dan Milner's (Liam's Brother) and guest-Dolphin's comments are the only ones that aren't based on pure speculation. Gareth, a self-proclaimed nautical historian, should keep his day job--please. Even a cursory search of Lloyd's registries wouold show that there was only one ship David (not "Davey," --he was in Congress, after all) Crockett, and the one built in Mystic, CT did indeed have a Captain John Burgess.   

Doerflinger collected the lovely song, it does not, when sung by someone who cares, sound like a rugby song, and yes, the folk process has been hard at work with this puppy for most of the 20th century.

There are plentiful sources to document this song completely, in all of its permutations--please stop guessing--this is how rumors get started. Oh, and while you're at it, don't bother to even read this post, because Milner and Dolphin are the only ones worth listening to.
--Cheers!