Personally, I think that it is plausible. Teenagers' brains don't work the same way as adult brains and I kind of hope that their is more to this story than just the cheeseburger and that the bullies didn't intend for things to get that far out of hand, but I believe that this sort of situation could happen. And I would believe that it could happen if you changed details to make it fit my own religion.
As far as why the director would continue to harass the mother even if she isn't currently planning to sue, I can think of a few problems that would be created by this situation beyond the possibility of a lawsuit. First of all, I'm not a parent yet, but I think that I would definitely reconsider sending a child to a camp where the sort of bullying happened and where the counselors heard noise from a tent or cabin, wasn't certain if it was laughing or screaming and decide not to check up on it? For that matter, I can think of some situations that might set young teenagers into bouts of loud laughter that I would want stopped as well. Secondly, I would imagine that an insurance adjuster who heard about this sort of incident would be reconsidering the camp's premiums. Also, I know that there are certain types of insurance where you are supposed to report incidents that might result in a claim immediately so that the insurance company can instruct you in how to proceed. If that was the case I could see a director panicking before or after doing that and engaging in the type of behavior described here. In situations like this it is much easier to blame the victim than to admit that something this bad could happen.
In both the first and second situation, it would be much better (for the director and/or owners) if the director could get the victim's family to admit that she over-reacted to something and that it didn't really happen like that and an impatient, immature, or inexperienced camp director might react inappropriately to a circumstance that he or she probably never imagined would happen as his or her camp.