Ester Derby has a post about a senior manager who was unwilling to talk to his VP to modify a commitment. The senior manager committed to deliver a special project, then after evaluating it, recognized that the project didn't make good business sense. The senior manager refused to talk to the VP about changing the commitment, ostensibly as a matter of integrity.
If I were the VP, I would expect the senior manager to give me the new information, so we could make the best decision for the business. I suspect that the senior manager's integrity issue is more a question of fear. Certainly the senior manager's integrity would suffer equally from knowingly making a bad business decision.
Sometimes a leader needs to make the decision to take the personally painful path for the greater good of the team. Integrity demands it.