Yep,, the sudden immediate stress of a very dire situation can often result in a person freezing,, or failing to act quick enough to properly defend themselves or prevent bad things.
Combat vets will tell you how often the FNG will get killed the quickest because of this.
LEO's are no different.
And MANY,, MANY gun owners & such feel the same way. I know I used to think; "I can handle myself if something bad happens." I knew I shot a lot,, (on a range) hunted a lot, especially with a handgun. And I had the mental attitude that "I was very capable."
Then I tried a stress induced game called USPSA. I found out how good I was NOT!!!!!!!! Many will poo-poo the idea of such games or competitions etc saying it's not the real thing, or it doesn't help etc. I will QUICKLY agree that it's not the same thing,, but it's a way to safely train your body & mind to become "motor memory friendly" with a bit of stress, AND teach you fast gun handling skills.
We have a saying in USPSA. "When the buzzer goes off,, the brain disengages!" And this is with a pre-planned idea of the stages.
There is not an inexpensive way for people to regularly train a LOT to be truly ready for the sudden event of a bad situation where it can mean life or death.
But as Blume mentioned,, there are schools & such,, or as XUSNORDIE mentioned,, the FATS training. But just doing these things is not regular & often training enough to where your mind & body develop the motor memory skills it needs. This is where games like USPSA, IDPA, can benefit people a lot.
I've often said that all police departments should be requiring every LEO that is required to carry a firearm to do a minimum of a full day of stress induced training (like USPSA or IDPA) at least once a month! In these games a timer induces stress, because part of your actual score is calculated using time. In USPSA,, it's your hits on a target,, AND your time that determines the score you receive. We have a saying; You can't hit slow enough to win, nor can you miss fast enough to win." You need good hits, AND a fast time to win. And if LEO's were judged by their monthly scores in a manner that would require them to achieve a certain level of scoring, then they would be MUCH better on the street. I would go as far as to NOT allow them to see a stage prior to having to shoot it. But I would also say that if they were to be required to do this,, MANY more would begin participating in games like USPSA to make sure they keep their job.
We hear it all the time. A "LEO was involved in a shooting. The suspect was injured or killed, or the LEO(s) were injured or killed."
Heck,, just last night,, the local news had a short story without many details,, where a local County officer was involved in a shooting. He responded to a call of a person randomly shooting. He arrived and a gunfight happened. The suspect and officer were injured, and taken to the hospital. The names of the officer & suspect were not released.
My first thoughts were; "How many shots did the officer fire after he determined he had to engage the suspect?" My second thoughts were; "Why wasn't the suspect killed?"
So,, it's not just cops who aren't gun people yet who have guns. I would suspect that a good percentage of the people here who own guns, and shoot regularly are better than most cops. But many of the gun people who do shoot a lot are also not well trained to be able to truly react properly & quickly handle a bad situation.
The BIG difference is we pay the LEO's to be our protectors AND they are required to carry a firearm as part of their job.
The minimums of LEO qualification is a joke to many of us here,, but it's still FAR from what they should do.
Those of us who do carry & practice & do things to make us better, are often the very ones who will fare better in a bad situation.