We try to cover all kinds of situations in our firearms training and have a very active program. The BIG CITY that we share a border with has their officers qualify once a year. We do an AR15 range, a shotgun range, a night pistol range, a stress pistol range, a state qualification range and two other combat related pistol ranges each year.
We shoot from inside the patrol car. Under the car. Behind the car.
We have a bail out range where the officers shoot from the driver seat then have to exit the car from the passenger side to get to cover.
(getting past the MDT, console and patrol bag on the passenger seat can be a challenge)
Today we did a pistol range dealing with point shooting at close range.
I did the research on actual police shootings and presented it to our officers a week before the range. I used NYPD /LAPD stats as well as local incidents to explain why we were doing it.
There have been several articles in the police magazines on the subject of late also.
My personal opinion and experience is that the vast majority of police handgun encounters are point shooting situations.
We have always done extreme close quarters point shooting but today we expanded it.
For the drills today we started with red guns to demonstrate action vs. reaction and to check weapon presentation of shooters.
The course of fire was contact range to 21 feet. Weapon retention was stressed. Lateral movement was stressed and used.
Prior to live fire I put electrical tape over the rear sights of the shooters Glock pistols.
All shooting was rapid fire.
Shooters were told to use the top of the slide as a visual reference and to keep both eyes open.

This range was NOT SCORED.
I think that is important. The scoring factor makes shooters even more nervous, causes them to slow down and negates the limited reality that we can put in the situation on a square range.

Targets were standard B27 with an 8" paper plate over the X ring area for visual reference.
Results were better than expected.Even my sub par shooters on standard sighted qual ranges were scoring good hits. There were very few missed shots among 32 shooters.
All the shooters reported that they enjoyed the training and found it to be realistic.
It was a good confidence builder.
There is a place for sighted precision fire and we do not discount that. There is also a place for rapid fire point shooting. I think we need to teach both and give them equal standing. Our officers deserve every tool we can give them.
Stay safe.

D.R. Middlebrooks has some good videos about this here.
It can be very accurate even at a long distance.

Sounds like you focus on some good training for your guys.

We do some of that style stuff, I end up doing a lot on my own.  Wish more of our guys did.

Anyway, keep up the good work man.  Sounds like your guys appreciate it.

Not too sure that the participants were doing true point shooting.  Covering the rear sights still leaves the slide and front sights available and is actually a form of flash front sight shooting, which is a very common technique that is taught.  Flash front sight shooting should not be confused with point shooting.  The basic theory behind flash front sight shooting is to align the muzzle and catch a glimpse of the front sight and cover the target.  The relationship of the rear sights is irrelevant as you do not use rear sights for this type of shooting.  Point shooting is a true natural alignment and point of the weapon without using either sights or the weapon at all as a reference for for aiming and the shooters visual focus is completely on the target.  A true example of point shooting would be with the weapon completely below the line of sight, or in total darkness where the weapon or sights cannot be seen.

Of course there are many different names and slight variations for these techniques depending on where you learned it, but your guys were probably not doing true point shooting from your description, but your drill and lessons definitely need to be a part of the regular teaching curriculum.  Good to hear that confidence levels went up.  Pushing guys outside of their comfort zone during training sessions is what its all about.  

American Guardian just had a show on this recently also.