I think most of the focus in arguments from Black musicians is culture and social history, not race per se. As I understand it, Peyton talks about the 'authenticity' of a Black American social response to music as being different to a non-Black one. I think he is saying the divisions between soul and jazz and hip hop and blues etc are not as categorical in the minds and ears of Black Americans. The music is heard in a more holistic way. I think the music of the sixties and seventies from Black musicians exemplifies that.
I think Payton is trying to get more "jazz musicians" to get back to that.
I also think he's right to do so.
I also think that everybody is going through the "growing pains" of the possibilities of assimilation made possible by about 35-40 years of relative non-segregation.
Finally, I firmly believe, and will believe into infinity, that "jazz" = "Black Music" in that no matter who did what when to what extent, it was always in reaction and/or in relation to to something "black". I have no problem with accepting that and then going on about my business, having no desire to "own" or "claim" anything other than myself inside myself, and as Duke said (more or less), it's highly unlikely at this point that we will be able to determine "whom is enjoying the shadow of whom" up/down in there.