Producer / Project Manager role clarification

How much creative control is typical for producers or project managers to have?

It seems like they are given the final word in a lot of gamedev areas, but aren’t required to have a proven record of experience or knowledge in any of those areas, in the same way everyone else is? Why is this?

(I don’t mean this post to deride producers / project managers roles - I recognize that they are critical to a game’s success. Good ones transform a team, and game, for the better.)