Most CEOs can recognize that a business decision can be absolutely the right thing to do for the business and not make that decision if it either would cost them (1) their standing with shareholders (2) their annual bonus (3) their standing with the board (4) their standing with internal constituents.
Again, you'll have to provide some compelling evidence or some very good arguments to convince me that the cases where the wishes of the board and/or the shareholders are in conflict with what is best for the business, are anything other than a rarity.
The key skill CEOs need to be CEOs can be summarized as: "How to become a CEO."
That's a very cynical and reductionist view. I prefer to think in terms of peacetime and wartime generals. In peacetime (ie. when the market forces make it difficult to fail for example because you have a monopoly), I think it's probably true that a very important requirement for rising to the top, is political skill. In a wartime, ie. in a highly competitive market, good business people rise to the top.
You fail to mention the 4th possibility (alluded to in the article): Market conditions sometimes change and the CEO is left with no good options. If you had a wildly successful business selling abacuses and someone suddenly introduces a low cost electronic calculator, there's probably not much you can do a CEO to prevent you market from shrinking. Of course you could try to change your business from making abacuses to making calculators in an attempt to hang on to your customers, but there's is also nothing about manufacturing abacuses that translates into creating electronic calculators, so the chances of that succeeding are slim to none.