I don't buy this. As CEO you have the right to say "You know what Big Important Customer? You're a dick and I don't want to do business with you."
That is a strategically stupid thing to do. You may not ever actually do it. But being able to do that without having to answer to anyone but yourself is enough. There's a very real psychological difference.
You have the right to say this while being the lowest ranking employee in the company, not CEO. But when you're CEO, you have other people you're responsible for, you hired them and they depend on you being able to run the business so they can feed their families. Saying "fuck you" to the customer who is bringing you 10% of revenue is not what CEO can really do.
That is a strategically stupid thing to do. You may not ever actually do it. But being able to do that without having to answer to anyone but yourself is enough. There's a very real psychological difference.