I find it more impressive they were able to manage a culture full of alpha dogs and make a productive business out of it. I wouldn't consider this type of culture as one to implement in my own company.
Google is similarly filled with smart, opinionated people, though Google culture seems far more team-oriented than PayPal does. The way we manage differing opinions is to run an experiment. Instead of saying "Okay, we're doing it this way," and letting the office politics determine what "this way" means, we say "Okay, what experiment could we run that would indicate whether this is a good idea?" Then we go off and run the experiment, and usually the data is clear enough that even the idea's most opinionated proponents and detractors end up being convinced.
"Strong opinions, loosely held" is a pretty good mantra for a productive team. A culture full of alpha dogs isn't necessarily a bad thing as long as they all respect the data.
The top-down corporate autocracy can often maximize synergy, but do so at the cost of individual/group autonomy. The free market maximizes autonomy, but does so at higher costs of transactions between groups. The wildly successful company can maximize both autonomy and synergy.