I've personally experienced working on the inside of a "culture of secrecy" in political organizations, in business and as everyone in personal groups / family.
My personal opinion is that this model does not work by default, it's not a modus operandi that is conducive to 'progress' (whatever the metric, be it innovation, profit, or even just the will to do things adequately).
I'm pretty sure there are other key points but my observation is that you need a strong leader, usually at the origin of that culture, who's able to mesh all subgroups together at a high-level (since they don't work together on a normal basis). What you observe is that leader's dream team (trusted advisors and insiders to the 'secret') taking various roles at various places in the structure to glue it all and maintain the secret while furthering core goals.
You also want a non-negociable acceptance of the culture by the people working there, meaning that you just can't tolerate any internal politics/wars and everyone has to flock in line. It's only ever possible to jail teams like that if there's trust in management (because eventually this is your career...) and nobody questions the 'why' or 'how'. You just do your job as best you can and forget about your high-level vision: big boss will decide (pray he thinks better than thousands of field engineers, few men on earth should be trusted with such decision power). Often people won't even know why X or Y got fired. It's part of the fear necessary to such a culture. Divergence is like random cancer in a culture of secrecy because nobody knows the big picture.
I'm more and more of the opinion that the kind of Apple built by Steve Jobs was 100% in line with his own way of managing (culture of secrecy, dividing or even gut open too-powerful groups to maintain his absolute might/vision, etc.) If you look at Apple's execs they're great soldiers, but not much of campaign-waging generals in and out of themselves (more beta than alpha, so to speak, perfect for a Jobs but maybe not a Cook). And I think it's painfully obvious, from the outside at least, that Cook just isn't the man to rule this Apple: he either must change it or give the reigns to someone more like Jobs (clearly only the former is a realistic goal, even for the next CEO and the ones after that).
Obviously this is all speculation and I might be wrong, but there are so many blatant red signs that I have little doubt that there's this culture/management fit problem within Apple.