When Aaron Rodgers returned to action after that broken collarbone in 2017 the Packers got beat. He played the entire 2018 season despite the leg injury and the Packers lost 9 games and had a tie. Rodgers didn’t like the offense and reports were he was butting heads with McCarthy. If the Packers felt it was Rodgers injuries that was causing the Packers to lose, McCarthy wouldn’t have been fired during the 2018 season.
So you don't think the broken collarbone and leg fracture affected the play of the player at the most important position on the field those two years? Rodgers wasn't himself, and that had the greatest impact on Green Bay's success.
Again, the Packers were 4-1 in 2017 before Rodgers went through the two injuries. It's not like they were playing bad up to that point.
It's no surprise that McCarthy and Rodgers butted heads when things were going poorly. Obviously, Rodgers not liking the play-calling and changing the plays didn't work out well for the Packers. It's possible that McCarthy was trying to call things to best utilize a limited player, while Rodgers felt he could do the things he had been doing.
Coaches often end up being the fall guy after a poor season or two, even if there are legitimate reasons for the lack of success.