I’ve argued (in Pantomime Terror) that Adorno wrote ‘Über Jazz’ as a way to talk about Nazi marching music. People forget that – even though by then he was mostly living in the UK – he published the essay in Germany under the false name Hektor Rottweiller. Reread in that light, his critique may be mistaken because of not attributing Jazz to the Black tradition, and maybe unfortunate for not being more obvious about its irony, but it is certainly comprehensible that he thought this way at that time. I remember reading an excellent essay by Evelyn Wilcox in Telos on this, so dug out the essay (nothing disappears now):
“His criticism was not directed only at Germany and certainly fits the splendid 1995 playing of “Tuxedo Junction” by the massed bands of the Guards Division at “Beating the Retreat” in London”
Wilcock, E. (1996). Adorno, Jazz and Racism: “Uber Jazz” and the 1934-7 British Jazz Debate. Telos, 1996(107), 63–80. doi:10.3817/0396107063
What I should do next is study the variations when he took the 1936 version and republished it in Moments Musicaux in 1962.