I too found my understanding changed dramatically when I looked into Aumann's original paper. Basically, the result has a misleading billing - and those citing the result rarely seemed to bother explaining much about the actual result or its significance.

I also found myself wondering why people remained puzzled about the high observed levels of disagreement. It seems obvious to me that people are poor approximations of truth-seeking agents - and instead promote their own interests. If you understand that, then the existence of many real-world disagreements is explained: people disagree in order to manipulate the opinions and actions of others for their own benefit.