I think in our case, the mother just likes drama. Her FB page is open and when I was told about the posts regarding my daughter I had a look. It's full of ranty posts about "messing with my family" type stuff. I was scum, DD was scum, we didn't care about our DD's behaviour, the school was shit, etc, etc, etc. she seems to air her dirty laundry on a half hourly basis with her hundreds of FB friends backing her up 'hun x'
School didn't know anything about it, I didn't know anything about it.
I actually felt quite mean about the way I dealt with it. I don't think DD is like that, she is generally nice and kind and none of her other friends parents have a bad word to say about her, but I didn't want to be that mother and I will never allow my daughter to be a bully, so came down really hard on her, when, as it turns out, the other girl had lied.
It all started because during an argument, DD had called the other girl a 'rat', however, we then discovered this was in retaliation to being called a cunt (a teacher had witnessed the argument). It was all very petty and teenage and silly, 6 of one and half a dozen of the other.
I suppose the other mother won't accept her daughter's part in it because then she'd had to admit she was wrong, and that her DD isn't the angel she thought she was. The other girl thinks it's great, she got away with lying.