If a company is so broken that promotions are decided based on factually incorrect information, there's nothing to do other than escape to a different company.
I'm talking about companies that are functioning okay, but they let the PMs drive what the team works on. A bad PM will send the entire team in the wrong direction and waste your time.
In the most extreme example, our PM would get distracted from the goals set by management and want us to do side quests all the time, so the entire team was constantly producing things that management didn't want while missing all of the things they wanted us to do. If your PM is the link between management and the team's directions, a bad PM will sink the team.