Reports: The officers who responded are the ones who write and file the reports. Some officers will blatantly lie on their reports, others will see a lot of stuff in a short period of time that they forget details or they become blurry. However witnesses aren't without faults either since they will undergoe something called the Rashomon effect, I also recommend reading up on the Rashomon effect. The Rashomon effect is where you can have multiple witness see the same event and when you ask them to retell what happened, every witness is going have a different version of the story they are retelling.
Another problem is that information collected from people is collected from telephone surveys and from news crews. There's nothing from stopping me saying "Yeah, my friend of a friend's cousin got his dog shot by cops" or "Yeah I heard from some guy that pigs kicked the door in and blasted his 3 puppies". Basically pepple who want to feel important in front of camera by saying something. The stats can be attributed to the rashomon effect. If there were a quote it would be Remember "there are lies, damned lies, and statistics".
also here is an article can chose to take or not to take with a grain of salt
http://www.washingtonpost.com/news/post-nation/wp/2014/09/08/how-many-police-shootings-a-year-no-one-knows/
I'm not quite familiar with the Rashomon effect, but I am aware that everyone experiences their own reality, which is basically what this effect sounds like to me, so I guess I'm a bit familiar with it. And you are absolutely correct about what the witnesses see and how police can and sometimes do lie on their reports, but now we also have to account for when police do lie on their reports and when certain details do go unaccounted for, and then when vital details are missing from said case that instead of this report being filed here, it instead goes here.
And yes, information is collected that way, but what I'm talking about is seeing the victim or a friend of the victim on social media spreading the word about whatever happened, and gaining awareness that way, which in my opinion is better than looking at a survey or listening to what some news station is telling me, because I'm getting, in my opinion atleast, the most truth out of the story from them, rather than some police sergeant on a podium lying through his teeth. And remember, they report
news, and not
fact