It's important to remember that it is possible to be too accurate in a gunfight. If you putting all of your shots in the same hole you're going too slow. If you're going outside of center mass you're going too fast.
I completely agree. I value accuracy highly and have had to work hard learn that combat accuracy does not require very small groups. Center mass is good enough if delivered quickly. The reason most of us don't shoot fast very well is we just don't do it, including cops. It is not a skill to be learned in a gun fight.