11:09 AM PT -- Civil rights attorney Ben Crump -- who's repping Andrew Brown Jr.'s family -- came on "TMZ Live" Tuesday to discuss the private autopsy results ... which he says jibes with what the family has seen, a flat-out execution.
Crump suggests there's a major cover-up at hand with this ... and it all seems to have started with what deputies told dispatchers when this all unfolded last week -- that Andrew was shot in the back, and not in the back of the head, which is what ultimately killed him.
It's just one more piece of an ugly puzzle that Crump says is coming together slowly but surely. Speaking of time, he made a point to explain why the Brown family is trying to get this body cam video uncovered publicly ASAP ... as opposed to letting it trickle out at the County's discretion.
He says he doesn't want people to forget Andrew Brown Jr. ... like so many other Black people who've been shot fleeing the police, whose stories came to light much later, after the fact.
Andrew Brown Jr. was shot 5 times during his fatal interaction with police, according to the autopsy ... and his family says it was one bullet to the back of the head that killed him.