Yeah, I don't have a problem with Barkley's opinion in general. I'm on record as saying Mike Brown is still head coach if the players hit their open shots.
However, the head coach has a position of authority. With that, he sets the tone and culture. If the players don't get along with or respect their authority figure, as human beings it will affect their morale and effectiveness. No amount of money or fame takes away your natural responses as a human.
Look at the players body language. From day one, it appears that a weight was lifted off their shoulders. This was on Mike Brown the leader. Not Mike Brown the man or Mike Brown the basketball mind.