More info from Walser's article — which I believe he got from Carpenter's PhD thesis:

"Carpenter called this a fragment of a capstan shanty, an idea corroborated by the repeated use of the word 'Heave'. He also noted that the song 'must be of Negro origin'."

It doesn't say, nor did Carpenter likely indicate, why he believed the last bit—or why he would necessarily stress that point at all.

People who have seen some of my other posts will know that I believe "John Kanakanaka," "John Cherokee," and "South Australia," despite the very strong references their keywords would seem to make to elsewhere, are based in Black song style of the Americas/Caribbean. They certainly may have been shaped through several other cultural sensibilities, but I believe the "core" paradigm (if you believe in such things) comes from there. This belief comes, not from very specific details of particular songs, but rather from looking at lots of songs and these songs within that pool, as a class. "John's a Rookey Ookey" *can* fit into that class, for me, but I have no reason to feel so positively as Carpenter that it "must"; I am trying to stay open.

It may be that Carpenter had other cues, like singing style. Or maybe he was just "closer", temporally speaking, to stuff he could compare it to and which was more obviously "Negro" than it might be to us today.