I will likely be flamed for this, but it’s not uncommon for the child claiming they’re being bullied to actually be the bully. You only have to look at some of the posts on here, from adults who were bullied themselves where they were the ones being accused, to parents of children who have been bullied who have gone through similar.
My DS was friends with a kid in early primary whose mother was constantly saying that he was being bullied, that all the kids picked on him, that he was a victim, except it was the other way around. He was horrible. Would openly pick on smaller kids and his mother would just say that it’s his venting his frustrations, but it really wasn’t.
We moved away when DS was in y3 so didn’t keep up with them, but some years later another mum friend told me that when he was 16 he’d told everyone he had cancer and had a year to live, and then he started a collection so that he could do things he wanted to before he died. Except it was all lies.
Don’t get me wrong bullying is horrible and if another parent had approached me about my child I would bloody well want to know what that was about.
But I do think that sometimes it’s not all that black and white.
But yes, if this girl had been making unfounded allegations about your DD I would tell the mother that you would no longer be allowing the friendship, who spare her DD obviously. We’d soon see how that panned out.