Yes, the Cajuns replaced carrots with bell pepper. I presume because carrots wouldn't grow properly in Acadia.
As for the black=American problem, I can avoid that. What I meant by "Jazz owes a debt to Africans" is that the roots of Jazz include influences from pre-slavery African culture. Obviously, the experience of slavery and its aftermath played a huge role in black culture, but there were important seeds that came over with the slaves on the ships.
I guess what I'm saying is that America, in all its forms, is a relatively recent product, made up of many different parts that can be traced around the world. From a cultural standpoint, I don't think there is such a thing as "American Exceptionalism." We're a mutt culture.