Most definitely, they do. And let's admit there is an antagonistic relationship between police departments and black men that leads to innocent black men being shot and--yes--murdered. We practice a destructive form of denial if we try to pretend that racism isn't a part of it.
All that said, I can't get on board with BLM for one simple fact: they only get involved when some black lives are affected. Namely, those killed by law enforcement.
For example, if you are a black man shot near a BLM protest by someone not carrying a badge, your shooting will not get a hashtag, let alone one that reads #BlackLivesMatter.
You're just #MondayNightintheBigCity.