I think your last paragraph aptly explains it all. A fish rots from the head down. If we take a broad and intangible concept like "culture" and reduce it to its mechanical workings, we see that it's usually the net result of everyone's incentives. If people at the top are setting perverse incentives, then their lieutenants will meet those incentives, and on down to their lieutenants, and so forth. Those at the bottom of the ladder will model the behaviors of those they're seeing get ahead. And one day, when they're moving up, they'll carry out the behaviors they've been conditioned to exhibit.

The other tricky thing about culture is that it's a lot like trust: very hard to earn, very easy to squander. Once lost, it's difficult -- sometimes impossible -- to recover.