I'm sure there is some truth to that statement.
It is really difficult to quantify a manager's impact on a team. For one, there are times when we don't know whether a move, like a sac bunt or a stolen base, was called by the manager or the player acted on his own. For two, sometimes the manager makes absolutely the right call but the players fail to execute, or vice versa. For three, we have no way of knowing what might have happened if a different call was made.
All we have is the difference in win expectancy between one decision versus another, which is very, very small, and the fact that managerial skills show no ability to repeat.
I am not saying that a manager's decisions make no difference in a game, just that they don't impact the game as much as most people think they do.