Eric, I am often silly and pretty often wrong, but in this case, I'm not kidding and my ideas come from long study of Japanese culture. I don't think haragei is used at all as a martial arts term. I know of it only as a cultural mechanism.
The Japanese believe that all people are connected through the hara to all other people. The group and maintaining the group is far more important than any individual within the group and disagreements within a group are far more worrisome than any belief that the group's direction might be "wrong". What's "true" or "false," or "right" or "wrong" is often less important to that culture than how everyone in the group feels about an issue. So every individual in a group can say "yes," but in the end the entire group can say "no."
Therefore, whatever any one person says may or may not be true: tatemae is what they say in public, for the group, to keep harmony and preserve everyone's feelings of belonging and loyalty to the group. Honne is what they really believe. So they don't just have "true" and "false": they have a sort of "truly false," "falsely true" and "truly true," the latter being extremely difficult to discern for anyone not intimately connected to the group. And the way to really connect with the group is through one's own hara. So haragei (belly art) refers to the art of perceiving through the hara what people's (the group's) real meaning is. Someone who ignores the surface "right" and "wrong" and understands through the hara is called a "man of hara." He can listen to the various factions in a disagreement, "stomach" them, and come up with a solution that will satisfy the greatest majority of the group. Those who still disagree can either "stomach" their feelings about it and go along, or else leave the group.
Haragei is subtle attention to people's very subtle cues about what they really think or want. One example was a politician who, during the lead-up to WWII got up and spoke fervently in favor of going to war, but because he repeatedly blinked his eyes as he spoke, other politicians were able to understand that his real belief was exactly opposite what he said. Still, the group decided to go to war.
This kind of thing was much more effective before the war because of the relative lack of distractions. So many people were packed into such small space and spent most of their time interacting directly with people, all of whom were more frightened of disharmony among the closely-packed people than they were of not being "right".
Now, with computers, cars, movies, TV, and all that, haragei is a vanishing concept in Japan. The younger generation is far more apt to speak their true mind, but in a closely-bound group such as the monjin of a dojo, it can still play an important role.