Crouch would disagree with me, too, but jazz ended a few years after World War Two. Bebop was the death knell, as jazz became less about dancing and more about theory, chops, breaking boundaries. (This is not to say that it's all worthless after that, but it's not jazz, just as rock and roll is not blues -- related, common roots, an offspring of blues even, but not blues.) Some of it is related to jazz. The cool stuff that came from Gil Evans and Miles obviously owes a great deal to Ellington, but it is essentially chamber music for jazz instruments. For too much of the jazz press, jazz is an anything-you-want-it-to-be category. Any thing that's not explicitly not-jazz is jazz. Crouch is an antidote to that.
As for the racial aspects, jazz is, in Crouch's words, "Negro music." Whites have made great contributions, but it's not their music -- any more than Bossanova is North American music because Stan Getz played it so well.