True, but in this case they'd have to be totally brain dead not to realize something major was up after Peter got caught in a serious lie, one he'd made a really big deal about (the whole point of the meeting, after all).
Unless he had amazing protection from someone senior and powerful enough, he would be dead meat.
In this special case, where he called a meeting on the basis of a lie about an important thing and was caught out on it?
I agree, it would be awesome, but incompetence plus industriousness at this at this level is seldom found. He wouldn't have been caught out if he hadn't moved to actively trying to get rid of Bobbie.
Except that path, in the organization outlined above, will lead directly to you getting fired.
Your boss spends more time with his boss than you do, and will monopolize the information flow. If you make your boss feel threatened? You're done.
Bad review with comments about workplace manner and ability to get along with teammates - BS "personal improvement plan" with vague metrics - wait 30 days - fire. It's that easy if someone's threatening to expose you for the fraud you are. Kids to feed and all that.
1) The overwhelming majority of information they see is information provided by Peter.
2) They don't really care that much as long as it doesn't screw up their universe.