It is appropriate to conduct an investigation to determine whether or not the shooting was as it appeared (an act of legitimate self-defense) or something else (a murder made to appear as an act of self defense). It is most certainly not appropriate to bring any sort of criminal charges unless and until evidence supporting the latter theory is discovered.
Of course you're right, and I spoke in shorthand, in that to make the decision to go to trial an investigation occurs, suspicions were raised, a case was presented to the grand jury -- all of that preceeded the trial, of course, and I therefore presume that the investigation raised serious questions regarding the facts and did not provide clear answers.