I'm no psychologist but there may be some people in your organization who professionals might call "passive-aggressive." They'll agree with you to your face and then complain about you or disagree with your decisions behind your back. These kinds of people can be a cancer in your organization.
Sometimes the challenge you find is that a few of your top performers - your superstars - may be the passive-aggressive ones. They do great work but their bad attitudes or behaviors are negative to the overall success or culture of your company. You can't allow these prima donnas to get away with their bad behavior.
I compare these troubled superstars to athletes who think they deserve to be treated better than everyone else on their team because they're very good at what they do. Sure everyone needs to be managed or motivated differently but there always need to be standards guidelines and rules that no one is exempt from.
Creating different rules for different people creates first- and second-class citizens in your organization. That's just unfair - and is no way to run a business.
Addressing the Elephant in the Room
Even if your superstar can't see that he or she is the elephant in the room everyone else can. It's your job to deal with that elephant.
One way to deal with it is in a performance review. Ask the person to outline their goals and to assess themselves on how they've measured up. Then ask them to identify their strengths and challenges and have them choose a developmental focus — what will they do to better themselves? Finally, ask them where they see themselves in the future.
You should also do all these same exercises related to this person independently and then compare your notes about the person with their own observations. Let them talk and then share your agreements and disagreements. This should bring the elephant into your superstar's sight. Talk through the disagreements and highlight the impact these disagreements might have on their individual performance as well as the organization overall.
Try to help the person understand and empathize with the rest of the people in the organization so that they can objectively see how their behavior affects other people. Do this by asking questions not by lecturing. This way the superstar will be more motivated and invested in the solution. If they are unwilling to change you must remove them from your organization to protect the integrity of your culture.