From Harry Binswanger's article, Just Pay for CEOs: Why Some CEOs Deserve Huge Salaries
The fate of the whole company lies in the CEO's hands. Only a very, very few people of those who'd like to make the high salary such a job has to carry can demonstrate the outstanding vision, leadership, adaptability, judgment, and integrative ability required.
Another way of stating this is that the CEO of a "large company"-- which is what the claimed statistic deals with--has a lot more than 300 employees, and the CEO is the man in charge of every one of them.
Here is a recent post that I just came across on the subject of CEOs earning their page: CEO Pay: Money Well Spent