It's true, although obviously it applies to the both sides. In fact, BLM protests were caused by exactly the same mechanism you're describing - liberal media was creating false narratives about police brutality towards black people.
"Transgender murder epidemic" is an even better example, it was completely made up by the media. Look up the numbers and compare them with the general population.
The difference is that the criminal justice system is supposed to address every single case. Any individual case of a public prosecutor refusing to prosecute a murderer (because they're also employed as a cop) is an injustice at the scale of the entire jurisdiction. Statistics on the race of the victims aren't actually necessary to get outraged. So your argument, at best, applies to the political framing of the subject rather than the core issue.
For many people, the idea that black people don't commit crimes at a higher rate than others goes against their every-day experience in the USA.
Maybe your response is ironic: I genuinely can't tell. But clearly "my every-day experience justifies my actions regardless of the facts about (my view)" is not a fair rebuttal, because anyone can make that claim about anything.
"Transgender murder epidemic" is an even better example, it was completely made up by the media. Look up the numbers and compare them with the general population.