What do you care if they get paid more than you? Do you care that they can out bowl you? Do they care that you can out chess them? Life is a marathon, you don't win a marathon by coming first in the race. You win a marathon by beating your last time.
Don't misunderstand, I'm always competing with my last paycheck. I always want to be getting paid more. I just don't care about other people's salary and if our responsibilities are lesser/equal/greater.
For me its all about optimizing the things I can control. I can control my future paycheck, and I can control how much effort I need to be putting in from week to week. I can't control someone else's salary, and it can't negatively effect me, so why expend the energy thinking about it?
Meanwhile: Responsibility != Effort.
For me its all about correcting mistakes with the least effort possible (I'm lazy you see). Also, if I'm paid the same, and I input less effort, then I'm technically being paid more :)
I would way rather put in the minimal effort required to question and correct (i.e. "manage" as you put it) an error upfront while its an idea, whoever's idea that might have been, rather than to put in the effort to correct the error while shit is hitting the fan.
This is just my personal preference. Your milage may vary.