I'm not sure if Bar Sinister was referring to non-profit organizations as they operate differently than for profit corporations.
Not on an organizational level.
Every BOD has a Compensation Committee that sets the policy for the company. More often than not, the BOD will set the pace for Executive compensation and/or salaries above a certain level... Management will set the compensation for all others below that level.
In the end, the message is this: A CEO cannot set their own salary unilaterally or arbitrarily... The only opportunity wherein that might occur is when the CEO is a majority shareholder (and controls the BOD) or they are the only shareholder.