What's the use of paying a coach if they don't give you any advice? Of course they are influenced. Their music choice has always been the same pattern after Mozart (with wasn't Montreal's idea nor them). And the "they have their own artistic vision" is part of the marketing to sell their artsy "contemporary art" programs, if you didn't notice yet. This year; they agreed to do Fame though they hate kitsch and fear to look ridiculous. They also agreed to get rid of Christopher Dean because it was the French fed idea and that their coaches are in war with the French fed.
From the outside, regarding what happened with V/M, the coaches and them, they're not rebels.