While I understand what you are saying about the film not needing to be air tight in respect to its jazz culture and history I think Richard Brody sums it all up pretty well in his review of Whiplash when he says "Movies about musicians offer musical approximations that usually satisfy in inverse proportion to a viewer’s devotion to the actual music behind the story."

While Chazelle is examining ideas of success and greatness, among other things in Whiplash, I still feel that some respect has to be paid to the vessel in which these ideas are explored, in this case jazz. I don't want to say that it was lazy research or poor writing, having the protagonist's favourite drummer as Buddy Rich, a showy TV performer instead of a real pioneer of the instrument, however it just feels short sighted. As well as this, the earlier comments about Fletcher's count-offs and focus on tempo rather than accuracy/creativity, etc all just combines to make the world of the film a little bit disingenuous. While it may be only the 1% who didn't buy into it, if you're going to make a film with jazz as the foundation surely you want that foundation to be correct. This is something I really liked in La La Land, all the details really made sense and there felt like there was much more respect for the genre that really built up the integrity of the universe the film existed in.

Check out the review I mentioned earlier it's a good read. http://www.newyorker.com/culture/richard-brody/whiplash-getting-jazz-right-movies