What justifies a shooting in the eyes of the prosecutors so that they will quickly come to that conclusion instead of taking their time and making the whole thing go thru the courts.
There are a thousand and one reasons which contribute. Briefly though you want to try and preserve your mantle of innocence to the extent possible. There are a whole lot of things one can do BEFORE a shooting ever even occurs. Avoidance, evasion, words and objects are things one can use before force is ever employed.
Even if a state has a "Make My Day" or "Stand Your Ground" law, if there is the opportunity to make egress or retreat to safety, then do so.
Carry a gun, then carry a cell phone. He who dials 9-1-1 first wins. Conventional wisdom holds that "bad guys don't call 9-1-1". In truth, even cops will tell you that bad guys call 9-1-1, but mostly to try and hurt "the competition". Doesn't matter if "no one saw you", the rule of evidence holds that there's always one more witness. If you see two witnesses, there's a third one you didn't see. However, if you see no witnesses, there's still one you didn't see. If you call 9-1-1, there's an increased chance you'll be viewed as the complainant rather than the respondent.
While I think talking to the nice officers in the immediate aftermath of a shooting can be less than ideal, a response of "I ain't sayin' nuttin' till I talk wit my loy-yah" isn't perhaps the best possible response.
Indicate that you're the victim, offer to assist in making a statement, point out exculpatory evidence and witnesses, indicate that you want to confer with legal counsel, then STFU.
"Officer, that man tried to kill me, and I will sign the complaint. There's his knife on the ground. That lady over there saw what happened. So did that clerk behind the counter. Officer, I'm sure you understand the seriousness of this situation. I will sign the complaint, make a statement, and cooperate with the investigation once I've had the chance to talk with a lawyer."