Most of these so called "Krav Maga Techniques" taught to incorporate judgment and combine Hand to Hand Combat with the use of a Pistol or an assault rifle are just extra drills that teach the student quickly how to use his judgment at all time possible.
Also there is the consideration of how much time you have to train a group, what kind of a group is it, etc. The assumption that pistols alone give greater advantage to officers over unarmed criminals does not take into account scenarios of reaction time distance, or the possibility that their attackers might be armed as well. So it is important to have a challenging draw time and speed shooting with yet sufficient accuracy.
If you have civilians that do not carry guns, you could teach them what to do and how to use their judgment if they acquired a weapon during a fight or teach them what to do without having pistols. At the same token, it is preferable to teach police officers what to do if they did not have pistols in their possession, since self defense should cover all possible scenarios where you need to use your body.
The bottom line is that anything should work if you hit your opponent's pressure points before he hits yours and you maintain the leading advantage by either giving the first devastating blow, or keep scoring and not letting him score, taking into account the possibility of other possible opponents at the same time.
In teaching officers how to rely on their pistols the instructor needs to test a projected hypothetical scenario using 2 proficient training partners and see which one has a better chance the one that move backwards to draw his gun or the one that is repeatedly chasing and stabbing.
Of course if you are assuming you blocked the knife, and delivered a punch as the same time to break your opponent's train of thought and slow his system down giving you time to move back, it might be a preferred option of judgment in a situation where you wanted to draw your weapon and respond to a greater danger like multiple opponent.
But keep in mind that you have to ensure you will not get stabbed in the attempt to do something that takes longer amount of time. Also there is the consideration of how much time you have to train a group, what kind of a group is it, etc.
Generally, what I think is important in Krav Maga, is the attention to the basic kicking and punching techniques, and teaching their applications and their purpose, teaching and explaining the differences of the applications according to the instinctive nature, and the distance factor.
Being aware of the reaction time and looking for the most instinctive and efficient response, you need to take into account that your opponent is at least as good as you are, but does not necessarily follow the same principles that you are. You need to be able to develop the tools for appropriate response.
So if the basic principles are applied with logic, and there is no gross negligence of the principles which lead to ignoring the best capabilities and best sequence and hierarchy of prioritizing, then I feel that the person is doing true Krav Maga.
What you want to avoid as an instructor and student is training methods that might develop bad overall habits. You do not want to develop a bad habit of blocking a knife and moving backward to draw a weapon leaving the outcome of the confrontation for chance. I would prefer to have a complete analysis of each approach before attempting it.
The question is how many times in reality you need to move in block a knife stabbing attempt, and counter attack and then jump backward giving your opponent time to recuperate.
The question is why you managed to knock him down in your 8th attempt and not the first or second. The answer appears to lie in the quality or striking and the quality of the protective gear he is wearing.
The gear would have the same effect in all the strikes since he is not taking it off, and as for the quality of striking you need to perfect it so you will strike a knockout in either one of your 1-8 strikes.
Also, as a training method, it might be preferable for this approach to demonstrate the fact that you are not being stabbed but at the same time you do not cause damage to your opponent, but on the other hand in reality you might have skipped a chance to knock your opponent out with the first reach to one of his pressure points since you stressed too much the need to move in and out and got the habit of doing so.
Krav Maga teaching of defenses vs. chokes besides the low probability that an officer would be grabbed in a choke hold is to make the difference from a learning point of view.
While Jujitsu has many ways to get out of a choke, Krav Maga tried to look for the easiest ones that would work as an instinct. While karate preferred a strike, Krav Maga claimed it is not instinctive while gasping for air.
Krav Maga teaches two methods, the pluck which is more instinctive and creating leverage on the opponent’s wrist using your neck and your arm extension in an upward motion.
Striking is taught immediately if you recognize the intention of your opponent to choke you off hand and as a counter attack if you executed a release move.