I don't have much to say that hasn't been said.... I am so sorry that this occurred. It is one of the hazards of what we do. No matter how awesome we are, Mom/Dad always believe little Johnny's story.
I am glad to hear that you have documented everything. That will be huge if anything ever comes of this. Note that I said "IF"! I would continue on with your business. Advertise, and run as normal. The other parents don't need to know why he left. Try not to lose any sleep over it, hard as that may be. IF they end up taking it farther, I would consult a lawyer, just in case.
Good luck, and prayers that this all blows over!!!