Not so sure I agree with that, I apologise in advance because I am going to totally butcher how I explain my thoughts.
If a manager has a proven record of winning titles, trophies with different groups of players then he becomes the constant in the development of a team. Track record, pedigree, whatever you want to call it. If his new players are unable to follow those plans and have a track record for poor decision making, sudden and extreme dips in production then it becomes easier to "blame" for want of a better word the players.
I think it's something that baseball fans have tried to appraise in hitting coaches, how much of a difference can a good hitting coach make to an average batter, most of the conclusions were that you can improve technique but it's incredibly hard to coach players out of unhelpful mental processes.