As a general rule, yes, the prosecutor does have the option of looking at the evidence and determining whether or not to charge. Just because the shooter claims it was a good shoot don't make it so, though.
One of the points that I think Frank is trying to get at is this: The shooter is not the final arbiter of whether a shoot was good. That role falls to someone else (judge, DA, jury, etc). Bear in mind that the prosecutor is not required to believe the shooter's side of the story. If I shoot a BG, who survives, and the BG survives and tells a different tale than I do, a prosecutor could well decide just to let a jury sort it out. (Sometimes, that's the politically safe move.) There could also be all sorts of political pressure for a DA to charge.
No one ever said it was up to the shooter to call it a good shoot.
The prosecutor is required to take the evidence presented upon them to make their decision. It does not mean 100% of the time they will believe the shooter but the other side of that it does not mean they will not believe them either.