Claims that mental illness not linked to violence rings false

I seem to have read many articles about mental illness that make the point that, to quote one, "people with serious mental illness are more likely to be victims of violence themselves than the general population", and furthermore, "people living with mental health conditions are no more likely to engage in violent behaviour than the general population".

I can believe the first of these claims, although it glosses over the fact that those with serious mental illness are a very small subset of the general population, so that, as a percentage of the entire population of victims of violence, their numbers are tiny.

I find the second claim to be less instantly believable, though, so I tried to get to the bottom of it. I found a meta-analysis by the Treatment Advocacy Center, which looked at various studies around the world on the incidence of violence among schizophrenia sufferers, and reached a "conclusion that I did not want to reach", namely that "there appears to be a relationship between mental disorder and violent behaviour", particularly during times when they are not being treated.

How does that square with the claims so often put forward by mental health advocates? Well, I'm not sure. Are they cherry-picking results? Are they just guessing, or making unsupported claims that back-up their own agenda? Who knows?