You say that she may not have understood the gravity of what she said, I'm not so sure.
She may not have understood the nuts and bolts of it but she will, from school, know that it is a very serious thing to say and that, of course, is why she said it instead of calling him a fucker or twat.
She knows men are scared of it. What if she had said that claim to him when they were in a shop or a doctor's waiting room.
She may not know what it is like to be accused of something and to have no-one believe you but she needs to know before she becomes a girl who lies and makes false claims.
What would you do if it is your husband, dad, or her teacher next. She only needs to say it to someone who believes her and an innocent man is ruined.
The remedy for that is in your hands.
Tell her dad, her sibling, her gran, her best friend something horrible and totally untrue about her. Let her feel the full weight , upset and frustration of trying to tell them that it is untrue.
That might sound harsh. It is but sometimes, only nasty medicine will do the trick and I have a feeling that all the explanations in the world won't make a jot of difference to this girl.
By the way, I sincerely hope that her ipad is in the bin.