In days past, without contradictory evidence such as video, statements were all investigators and prosecutors had. There was probably more of a bias in favor of trusting police officers, especially when it came to killings of minorities, in the past. If the story met the legal requirements, there was no further examination. In some cases, an officer's fear was all that was used to justify the shooting. That's not today's world, but the mentality of an officer's statement being trusted first still prevails.
Update: This article explains all might not be as it seems in this case.
Mistakes aside, many are too quick to condemn the vast majority of competent, law-abiding, trustworthy, and disciplined officers. Before one condemns law enforcement as a whole, one must remember that these are a minority of events given the size and scope of the country.