How they act shouldn't lead to a different perception on whether their life has inherent value. This isn't just a socioeconomic question - the fact is that black people tend to be more likely to be punished more harshly (or indeed at all) for the same crimes as white people. Nobody is disputing here that poor black neighbourhoods have high crime rates - but that doesn't mean that black lives should be considered less valuable.
And hey, if the rest of the world started treating them like human beings, maybe that might start making a difference - when you grow up feeling like the cops could hit you, beat you or kill you for pretty much no reason, that's rather a disincentive to be positively engaged in your society. (To take another prominent case that emphasises the "no reason", a guy was killed in Utah in September. He was cosplaying and carrying a sword, and the cops shot him six times in the back. No charges were filed for this pretty much inexplicable murder.)