It's important to realize that the lie is probably not from the police as a whole, but from the officer or officers directly involved, with a healthy amount of CYA involved, realizing the screw-up. In such a case there is most certainly a loss of faith between the public and their police force.
Which too often seems to be the case in instances like this. I've seen cases where a guy was shot in the back and the police claim he was being aggressive. There's even cases where police dispute unnecessary deadly force when a man is cuffed and pinned to the ground, and then shot.
Police too often back each other up in these cases. If an act is performed in uniform as part of their job the whole police force backs him up, he gets attorneys provided by the police force, and it is in every officer's interest to justify every wrongful death so that when they have a legitimate case come up they don't have a history of unnecessary violence on their force.
Sure, the police were telling the story as officers on site reported it. But how thorough did they dig into it and investigate those involved of wrongful death? Is it in their interest to do that or to support the story?
I still maintain that had events actually gone down as presented by the police, their actions would have been 100% correct and justifiable. It's simply unreasonable (Keef) to wait for a cop to get shot and possibly killed before going inot actual defensive action. You're not going to recruit many policemen if that's the actual position of the law. It's not their job to face deadly force passively. It is their job to deal with deadly force appropriately to remove the threat to public safety.
Here is why it is unreasonable. They were told in advance that there was a man with a gun. They showed up and approached in a wreckless manner, as to be open in the event of a violent reaction. They put themselves in an unnecessarily risky position without cover.
They approached with guns at the ready to be in a position to accuraty fire a shotgun, not even a side arm, at the man quicker than they could say, "lower your weapon." Even our own military's rules of engagement require them to identify probable deadly threat when dealing with an unidentified target, often in the form of an actual attack.
The fact is they described themselves as approaching a man they believed to have a gun, not being otherwise aggressive, in a manner that does not indicate an intent to defuse tensions. They describe themselves as having shotguns at the ready, fingers on triggers and aimed, in a way to make firing the quickest response.
They also described the man as sitting on the landing, pointing the "gun" in a two-handed stance, at the officers. Images of the landing show railing on the side where the bullets came from. Images show impact points in the railing, far too low to be a center mass shot on a standing man. Just looking at the space the man was in when he was shot I was immediately suspicious of the police story.
Ultimately, all homicides should be investigated for their justifiable means. And no police, in the line of duty or not, should be exempt from that. They are trained and should have an even higher standard.