Your surprise comes from the fact that you're modeling an institution as a single person when it in reality consists of a hundred thousand people. It's obviously less mental effort to reason about large entities this way, but it's obviously much less accurate.

That's funny because institutions can only be modeled as a statistical average of all of the humans who contribute to a given property of the institution.

Untrue (there's plenty of emergent behavior in large organizations), and ignoring that, irrelevant. An obvious trivial example is looking at the property of consistency in actions: an organization consisting of a hundred thousand people is going to be far less consistent in many sequences of actions than any given person would be.