As a manager I am frequently in situations where I hear people say things or commit to things that I am not certain are correct or in our interest. Correcting the account or the expectations of others without undercutting a person who reports to you is probably one of the most delicate jobs a manager faces. Here's how I make my decisions about what to say and when to say it.
When the information is factually wrong:
If a person who reports to me conveys information I know to be incorrect and that information will impact a client or prospect materially, I'll step in an correct the situation immediately. In this case the correct information is more important than "face" or feelings.
When the information is not relevant:
If a person who works with me or reports to me insists on bringing up information that is not relevant or off topic, I will try to approach them after the meeting to encourage them to stay on topic. If I suspect that the behavior will occur, I will try to meet with the individual before the meeting.
When the discussion is personally or culturally damaging:
Sometimes a discussion can start out innocuously enough but be taken hostage by one person with an ax to grind. If that person starts denigrating the organization or other individuals, I'll make the determination as to the importance of the situation and either speak with the person after the meeting (and redirect the conversation) or directly confront the person in the meeting if the conversation is damaging enough.
The challenging part of "staying on message" within a team is knowing what messages and behaviors you can ignore, which ones should be dealt with privately and out of sight of the other team members, and when you should confront the other party with the facts and possibly cause them a loss of face. As a new manager, I too often would confront other people with information I had in an open meeting, losing a chance to build bonds and counsel people out of the limelight. This behavior causes two types of actions, neither of them good. People either decide to keep their opinions to themselves, afraid you'll show them up, or they ratchet up the discussion and every meeting becomes an in-your-face exercise.
As I've grown (hopefully) as a manager I've tried to learn what can be ignored, what offline counseling or discussion can be helpful, and when a direct frontal assault is necessary. A good manager will use all of these tools, and probably more, to help his team stay on task and on message. A poor manager will use only one, or none at all.