In the case of Nathan Phillips and the students from Convington Catholic, video evidence was available if they'd cared to investigate.
In other cases, they should have withheld judgement until they did know.
In other cases, they should have withheld judgement until they did know.
And I'm not just talking about the court of public opinion here— the point of BLM is that many POC don't even get the benefit of the doubt from law enforcement when lethal force is in play.
One does get that impression from a superficial examination of the stats, but Roland Fryer, professor of economics at Harvard and himself a black man from an underprivileged background, looked deeper and concluded that, if all other factors are the same, police are actually more likely to shoot white people:
https://www.washingtonpost.com/news/wonk/wp/2016/07/13/why-a...
(Postscript: in my personal opinion, this divisive issue is unproductive. Why can't we oppose the aggressive policing of America (a problem that undeniably affects people of all races to some degree) without making it a racial issue?)
There's a pretty widely-cited and thoughtful rebuttal to the Fryer paper, which I'd encourage you to read in its entirety: https://scholar.harvard.edu/jfeldman/blog/roland-fryer-wrong...
"Even if one accepts the logic of statistical discrimination versus racial bias, it is an inappropriate choice for a study of police shootings. The method that Fryer employs has, for the most part, been used to study traffic stops and stop-and-frisk practices. In those cases, economic theory holds that police want to maximize the number of arrests for the possession of contraband (such as drugs or weapons) while expending the fewest resources. If they are acting in the most cost-efficient, rational manner, the officers may use racial stereotypes to increase the arrest rate per stop. This theory completely falls apart for police shootings, however, because officers are not trying to rationally maximize the number of shootings."
"It is a failure of journalism that the New York Times heavily promoted this study without seeking critical perspectives from experts in the field. Fryer makes basic methodological errors, overstates the quality of his results, and casually uses the term 'racial bias' in a way that is nearly guaranteed to be misinterpreted by anyone who isn’t an economist."
"All lives matter" is not suggesting the "firetruck" should ignore the "house next door" (black victims of police violence).
BLM, on the other hand, is suggesting exactly that: the firetruck should ignore the white victims.
But your argument is against a strawman. No one is asking for white victims to be ignored, and no one is asking for "100% of coverage" to be about injustices against blacks. Obviously the lives of white people murdered by cops matter, but those murders get attention and sympathetic coverage by default. Those are the crimes where people start to ask whether policing as an institution needs to be reformed, instead of asking whether the victim was wearing the right clothing or was sufficient subservient or had just committed a petty theft. All that BLM activists and their sympathizers are asking for is to see similar coverage across the spectrum. That so many whites see this as an attack is just indicative of how much work there is yet to do.