Could be true. I've always heard the cause was Gene Roddenberry taking more of a backseat role, and new writers being brought on board (for less pay, no doubt). A look at the writers for each season shows quite a few new ones
(and Gene L. Coon using a Lee Cronin as a pen name).
I doubt the writers were paid less for their work in the third season than in the previous two years; union rules tend to keep those costs pretty stable, do they not?
A lot of writers who had previously written for the show were retained, too. D.C. Fontana, Gene Coon, Gene Roddenberry, John Meredyth Lucas, Oliver Crawford, Margaret Armen, Jerry Sohl, and Jerome Bixby had all written for the show at least once during the first two seasons. All but Sohl have multiple writing credits during the third year.
change was the show's production staff. Gene Coon was no longer producer (he left near the end of season two) and his late season replacement, John Meredyth Lucas, was not asked to continue in the role during season three. D.C. Fontana left her role as script consultant. Gene Roddenberry was executive producer, but in name only. Although all four of these people were still around as writers, none of them were around to re-write material to bring it in line with the series format and characters, and the show suffered for it.