OK, so you have a camp. You group the kids and give them some kind of fake task and expect them to learn leadership. Obviously this is a recipe for failure.

Because in a group, there can really only be one leader! So self-organizing ensures that the kids learn team work (hello, teamwork camp) but not that they will learn leadership.

Now, teamwork is a useful life skill and it sound like your DD could benefit from additional experience with it. Take that as your lesson -- dealing with stress, learning teamwork, coping with perceived and actual failure -- those are places to help her work on. And you have years yet to do that.