I haven't seen any memos from "Bread and Circuses" indicating a massive fight. There's a letter for WGA arbitration in which the two indicate they want to share credit 50-50 for the episode which suggests the opposite.
Inside Star Trek went into rather intimate detail about Coon's departure, anyway (and it wasn't a fight). I'm not sure Cushman can present much more than that. Considering the two collaborated on Questor only a few years later, as well as other correspondence, I find the idea that they had a blow-up pretty suspect. But, we'll see...
Considering how GR could mend fences when it was beneficial for him to do so (Ellison in the pre-TMP years), it could be he had to go to Coon hat-in-hand for the QUESTOR rewrite. Then again, it could be that the material actually spoke to Coon, because I find the QUESTOR antagonist to be just superbly realized, in part because of actor John Vernon but also because he is so well-written, and his dialog just HAS to be Coon's.
I figure GR had to be jealous of the fact Coon made his show work better in a lot of ways than he had set out to do, and maybe GR didn't like the comedy aspects either, unless the comedy originated with him (anti-Christian type sentiments.)
The fact Shatner has always been so unstinting with his praise for Coon (and that goes back to the 70s with his SHATNER WHERE NO MAN book, which has him saying something like Gene Coon, by leaps and bounds above everybody else, is what made the show work) has always been a pretty heavy signifier for me.