As a competitive shooter, I have helped a lot of cops learn to shoot. I could take the average guy who has never held a handgun and in one day I could teach him to shoot on a level that is above most in law enforcement. The only ones who are shooters are the ones that are ‘gun guys’ and shoot on their own. Most are of the pray and spray type.
My brother ran the DCPD shooting range for a number of years and told me the number of misses at close range is incredibly high. People panic and cops are no different unless they have that training so thoroughly ingrained they act reflexively to aim straight.