It seems CY's main point was that the call-and-response work song was originally African and came into shantying by way of African sailors. Others point out that there were shanties going back to the 1500s and that waulking songs are call-and-response work songs in the Celtic world, presumably unrelated to African models. I'd add to this that songs associated with threshing sometimes used call-and-response form. In Brittany, the came kind of Kan-Ha-Diskan that is used for plain dancing was also used to tamp down the threshing floor so that it would be hard enough to thresh on. Throughout France, and especially the northwest coastal areas, call-and-response is one of the most common types of singing, both for shanties and for other purposes. From all this, I just don't see any evidence that shanties ORIGINATED with Africans; there seem to have been call-and-response work songs elsewhere, and the shanty seems to have originated before Africans were a major part of the workforce.
CY's use of movies like Mogambo and Zulu as evidence is also a bit dodgy. Calling their tradition "centuries-old" and the song used to haul a rhinoceros out of a pit a "long drag chantey" makes it SEEM like africans invented the long-drag chantey centuries ago. But what we really have is a twentieth century movie of modern Africans using a song structurally similar to a long-drag chantey. It's not a centuries-old document, nor is it clear whether this tradition is connected to the shanty. It could even have been staged by the director.
BUT, I think it's fairly obvious that Africans, West Indians and African-Americans have had a huge impact on shanties, especially the English-language tradition.
Now for my main point: to say that historians and folklorists have ignored this is untrue. Every folklorist I've ever heard talking about shanties presents the evidence that Africans had a major influence, and talks about the theory that the name originated due to moving homes in the West Indies. Roger Abrahams has done some very important work on West Indian shanties (see his book Deep the Water, Shallow the Shore); I was just looking at his fieldtapes the other day, wishing I had a reel-to-reel deck! It's well and good to say that historians have neglected this and de-emphasized that for political reasons, but I don't think that applies to the African influence on shanties. The main problem, I think, is that most of what has been written on Shanties is quite old and the past few generations of scholars haven't written much on the topic. The standard books are still the ones by Hugill, who was neither a folklorist nor a historian, and wrote thirty years ago.