The way I look at it is that a manager can make decisions with wider scope, but the people under them exert greater control in day-to-day tasks over some narrower scope. In software development, for example, a manager might set goals for some project, but it's individual developers who are actually writing the code that usually have the most leeway to decide for themselves how best to solve some particular problem. (So long as it's within the bounds of what peer reviewers will accept.)

I think org charts would better fit how I think of the organizations they represent if they were drawn upside-down, like a tree.