I think there's some vagueness as to what "classical" is supposed to mean. As an ignorant child, I was under the impression that it meant the best material saved up from past ages, which had proved its endurance. The idea of "modern classical" was thus something of a contradiction in terms. Some of the people presently referred to as "modern", of course, like Stravinsky, are as far back in time to us as Beethoven was to him with respect to their early works. In this sense, jazz becomes a classical music simply by hanging around and having people nod at it now and then, and the reverent demeanor of jazz and classical DJs becomes appropriate -- we are among icons and sarcophagi.
Another sense of "classical", in America, was for many years "nice music brought over from Europe, not that awful stuff the lower orders make and like." This is why it was treason. I don't know how jazz fits into that -- uneasily, I imagine, nice and intellectual as it is. I can imagine the folks at Lincoln Center getting quite a transgressive _frisson_ when they play any.