Thanks for the post! I think this is turning out to be a fun question.
My inclination is to say that this was evidence that their system was bad, and the cheating was only "necessary" to counteract other flaws of their system, but still it indicates that the question isn't a crazy one.
Probably true, though I wouldn't be surprised if many of those flaws arose from cheating by the people closer to the top of the food chain. In many cases, I think that the most active cheaters might be the ones who come to occupy central positions in an organization. This also applies to the point about Civil Disobedience. For example, with "Jim Crow", I think there's a case to be made that the people who instituted the laws were also cheaters.
I'm especially glad that you included this point:
I don't think human organizations need cheaters and cheating to work, but it seems that allowing for the possibility of cheating may be necessary.
I was having similar thoughts when I was thinking about it last week, but I forgot to include it in today's post, and I didn't get it to this level of clarity. Just the possibility of cheating definitely changes the decision landscape. I like the way you expressed that point.