How do you react when someone in your team honestly owns up a mistake? Do you flip out or do you react constructively and help take corrective action?
What I've learnt from my personal experience is - if you become angry in such situations, then gradually most of your people (except for the really upright kind) will stop being completely truthful to you. They will start building elaborate lies to protect themselves and/or their peers/subordinates. Eventually, you will fail to get crucial information that would have helped you steer your project away from trouble.
If instead, you appreciate the honesty and react to it constructively, then you can be sure of getting the right kind of information every time.
The key then, is to be able to handle the truth dispassionately but constructively when it comes to you. This applies not just to managers, but to organizations as well. Organizations that are more open to honest criticism and incentivise (rather than penalize) honest data collection are bound to do well in the long run.