I'm inclined to believe that people with unmedicated mental illness in households filled with love and understanding will be wildly different from those in households filled with hate and ignorance.

That isn't to say that someone with unmedicated/undiagnosed mental illness in a home filled with love won't become violent, just that one will spur someone on to violence whereas the other won't (at least that's what I think, obviously violence is a trait many people come by naturally).