I have seen the suggestion in this thread that violent crime rates are not good predictors of police violence rates. Kriegman is using it as a predictor though. So this would be quite the challange to Kriegmans assumptions. And it is an interesting point. A point I do struggle with. Because I would say it is at least somewhat of a predictor: If you do not behave in a violent manner (even as a criminal, say stealing from your employees) there is not really a reason for police to meet you with violence. You are not a risk at that point. But if you commit crimes violently (say like a robbery) it would seem clear to me that police would engage you much more ready for violent defence/retaliation. You are a risk in this scenario. So it ought to be at least sonewhat of a predictor.
It is possible (and even likely) that there are some weak effects of violent crime rates that are statistically buried by stronger effects, but if we are seeing such burying, it largely fails to explain the trends that we see.
As for what explains the difference, I don't think it is as easy as something on a demographic level but instead something that is spurred on in large part by the relationship between police and their communities. I think that is part of what confounds studies which look at officers on an individual level (that is, seeing how they would respond to different situations). While racial bias certainly influences decision making to some degree, it is important to consider how race impacts the relationship between the police and their communities.