Blacks would like less blacks being shot by cops at the current rate
Here's what I think the situation is and what the black lives matter movement "is" and the problem with it ...
Black people are more likely to be stopped by police in many places. There are easily reasons for this that are not racist - responding to reports of crime, types of vehicle violations etc... and the simple fact that crime tends to attract police (you'd hope) so they should spend more time in higher-crime communities than lower-crime ones.
When stopped they are more likely to have non lethal force applied ... this can be a combination of attitude of those stopped or attitude and expectations of the police.
But as the report shows, they are less likely to be shot by the police and it is extremely rare. I can't imagine any officer wanting to shoot someone intentionally without justification - it is possibly career ending and life altering even if you are 100% in the right. Just look at the cop in Ferguson. As the report shows, I just don't think there is evidence that shooting of black people by white cops is the problem some want us to believe.
But, black people and the black lives matter movement have latched on to police shootings as something to use as proxies for their complaints over other things. Lets not forget that a lot of this was sparked by the Trayvon Martin case and specifically the altered audio played by certain media to present a false account and suggest racial motivation.
Things have snowballed from there and a hyperbolic language about how they are being hunted and killed by cops (to hear them tell it) has ramped up to become the "must be accepted narrative or else we'll call you racist". The blm supporters jump on any situation regardless of the right or wrong of the case itself and this obvious support for criminals and false claims puts many people off from taking the claims seriously.
Now, whenever anyone tries to discuss it, we have blm supporters trying to prove their claim by pointing to the greater likelihood of being stopped and use of non-lethal force and others pointing that out this doesn't prove the shooting claims. Again, this happened in Ferguson - we went from "white cops are hunting us down" to "but we pay slightly more traffic fines".
So to bring things full circle back to the OP about the sheriff's comments. He's right - what they are complaining about is BS and the anti-cop rhetoric is dangerous. It seems increased violence is the only place the blm movement has to go because they have set themselves up so that they can't back down due to the claims they have made and they can't prove them except to try and make it happen.
Wash, rinse, repeat.
The solution is likely to be smaller improvements to policing that are unlikely to be possible without a community that takes part in the improvements (i.e. lighter-touch policing is more difficult at a time when negative attitudes are being ramped up). The police can't step back from responding to criminal behavior and doing so will cost far, far more black lives if they do.
I think an important question to ask is what do blm actually want? Every time they are on TV they like to chant and shout accusations and repeat the claims (even often with the names of the discredited cases) but rarely have I seen anything concrete and actionable.
It seems to have gone from "we're going to shut this highway down unless we get what we want" to "we're going to shut this highway down". Is that it? Is it just the opportunity to inflict some disruption and inconvenience as 'pay back' to try and even the score? What's the end game and how do they think they get there.