It's not a matter of showing these people the facts.....they're not interested in facts. They're interested in feeling good about themselves and power....mainly power.
A dope like King has virtually no worth in life other than being part of some movement. So he, and others like him, will do and say whatever it takes to remain in front of cameras and microphones.
If all the (mostly justifiable) shootings of black males by the police stopped today, people like King would probably commit suicide. They want to be champions of the "poor and oppressed." If the "poor and oppressed" lives improve, their (King and others like him) sense of worth diminishes or disappears entirely.