We do know exactly what happened there. Multiple eyewitnesses were interviewed by the local authorities and the DOJ. The DOJ found compelling eyewitness and forensic evidence confirming Officer Wilson's account and found that the "hand's up, don't shoot" story came from people that either recanted the story later or admitted to not even being present when the shooting occurred. One Black man who witnessed the shooting told investigators, under oath, that he wished he had been armed because he would have shot Brown himself.
Brown wasn't shot for shoplifting. Brown was shot for attacking the officer who stopped him for shoplifting and attempting to grab his gun. Brown's DNA was found on Officer Wilson's gun holster and gun. Brown was shot once, in the hand, and turned to run. Wilson exited his car and began to chase after Brown. Brown then stopped running, turned around, and charged directly towards Wilson, prompting Wilson to fire again until Brown went down. Once again, all of these facts were confirmed by the local authorities and Department of Justice (federal). Eyewitnesses who saw what went down testified that they had been threatened with physical violence if they came forward with their story.