I'll tell you what, why don't you go in 'all guns blazing' and 'on the warpath' and refuse to leave until the teacher has recorded herself apologising a la Nick Clegg and the school has uploaded the video onto YouTube
. That will teach them not to mess with your son again.
Why is there an assumption here that the teacher has deliberately made something up? Surely she just thought he said something he didn't, it was investigated and now he has been cleared. Upsetting for him probably, yes, but not going to cause any long-term issues unless you make it into a big deal and make him a victim.
The teacher being stressed (and I'm not at all sure you should have been told that), and there being two other adults in the room makes me wonder whether it might not be quite a tricky class, perhaps a noisy one with comments being made here, there and everywhere, and that is why the misunderstanding arose. Maybe not, but no teacher, however stressed, unless to the point of psychosis, is going to make this stuff up for the hell of it. It will have been a massive ball ache for her and she would have nothing whatsoever to gain from it. Likewise, people saying she/others will hold it against him and mark him down are also being ridiculous - teachers are judged by the progress pupils make and would be crackers to mark kids down just for the hell of it, aside from any other reasons why they wouldn't do so. As for it being on his record, check that it won't be if you like, but that will make fuck all difference to his life, including while he's at school, anyway.
Finally, I would love to know what was said at the 'sit down' as that makes a big difference imo. Did she do a bit of an apology where she stopped short of actually saying sorry? That can be annoying, but unless she was rude or threatening or something I'd say the matter is now closed and you need to let it go.