You hate to say it, and it's not a solution to the general problem, but perhaps the best outcome for this particular case is for the girl and her mother to acce

You hate to say it, and it's not a solution to the general problem, but perhaps the best outcome for this particular case is for the girl and her mother to accept that the system is broken and realize the kid has been punished enough. Then lie. "No, I was lying before. All we did was sit down and talk in the park while having milk and cookies".