To me this sounds like a cry for attention? Not saying you neglect her, but perhaps she perceives it that way, especially with a boyfriend in the picture? Or perhaps there are younger siblings she feels are getting more attention then her. Usually when a child makes outlandish statements like that that are not true, she is trying to get someones attention. My parents were pretty dysfunctional when I was young. They were so wrapped up in their own problems, I felt like I didn't get enough attention. I used to fake injuries all the time to get them focused on me. Again, not accusing you of neglect, but sometimes we get so wrapped up in our own "adult" issues, we can perhaps not pay as much attention to our kids as we think we are. Is this a possibility?
I would also consider having her evaluated by a child physcholigist. Or all of you see a family counselor together. They may be able to shed some light on things for you.
Can you think of any reason she would be telling the school that you are hitting her, she sounds upset by something ..Does she see her mom on a regular basis and how does she get on there.?