I've heard a few of those as well. I can tell you that she is neither the daughter of a mob boss, nor a mob boss herself. As far as I'm aware she hasn't committed any sort of homicide.

That said, I believe she did take on at least one gang, but as I said she has not been convicted or accused of any sort of homicide so how she did it remains a mystery. She does appear to be a vagrant. At the very least she doesn't reside in Inaba itself. She has shoplifted from convenience stores and I once saw her attempting to steal money from an ATM.

So while some of the rumors are a bit off the mark, it's easy to see how they might have started.