There's no mystery: as Bruce mentioned earlier, Hewitt's setting was to a melody of his own; hence the copyright.  It was not in any way unusual for "composers" and/or publishers to neglect to mention the lyricist -particularly in America, where piracy of material from Europe was common (later in the 19th century, Gilbert and Sullivan had to arrange for some of their comic operas to receive their first performance in the US to get round that problem).  I have a note that the date for Campbell's poem is 1799 (though I can't remember where I got the information) so the dates fit.  As pointed out earlier, the poem was probably not set to Captain O Kane until 1822.  Incidentally, a 1788 Burns song, The Smallest Birds Rejoice was set to Captain Okean (Okain).

Malcolm