How strong is a confidentiality agreement within a company?

I agree with you, the situation is ugly. If you just back off now, it will seem to everyone involved that you are being a good sport but that you are tacitly agreeing with and accepting the poor tactics of those executive bullies. Not a good outcome. I think I'd be brushing up my resume, personally, but rather than just give you my own perspective on this, I thought it would be useful to forward your query along to Laurie Weiss, a colleague who focuses on corporate ethics and group psychology. Here's her reaction:

You don't say how many other members of the executive committee just “went along” with the bullies. They probably didn’t intervene in order to look like they are team players -- and to not open themselves up to attack. And what's more, they probably are not even aware that they did this.

This automatic going along with the crowd is called groupthink, a term coined by Irving Janis in a 1972 book, Victims of Groupthink, where he examined disastrous decision-making processes. If groupthink continues in your company you are likely to encounter a string of bad decisions that have the potential to destroy you.

If you want to save your credibility and stop this insidious process, your option is to do your best to divide and conquer. You need to have PRIVATE conversations with each member of the executive group. Focus on the damage that ignoring the bullies behavior will do to the long-term success of the company -- not on the damage it will do to your credibility.

If you can reach private agreements with each of the others on the team then go to the bullies individually and have the same conversation with each of them. You stand a good chance of getting them to reassess their behavior if they don't need to face public criticism.

You can't undo what has already happened, but you can use it as a platform to interrupt the tendency toward groupthink and reestablish your own credibility with the group.

Good luck!