The ones that would become leash shy from being jerked around like that have long since been weeded out of the population more than likely. I know less about police dog training, but I would hazard a guess that it is a lot like police horse training in that the the ones that cannot handle the pressure are culled. My aunt had a cull, he had a weird switch where he'd bite under pressure. He never made it to the higher training because he couldn't handle it. You could probably assume (although I am wary of assumptions) that the culls are probably dogs that would not react appropriately to being hung by a leash. Not to mention the fact that police dogs are generally bred for the vigors and stresses of their work. Not generally the type of dog that is going to become fearful of something easily or they wouldn't be able to do their job.
Do you know what collar conditioning is with field trial dogs? It looks absolutely terrible, but very few dogs cannot handle the training because it is with a purpose of teaching the dog how to handle pressure. When conditioned appropriately very few dogs become collar shy, although it does happen. That doesn't mean you can put a collar on a dog and use it without the dog becoming collar smart or shy. The dogs are conditioned to accept and understand the collar and what it entails. Dogs that cannot handle it are culled from the program.
Smacking a dog in the face for playful nipping is an escalation beyond what the action deserves. It shouldn't be the first resort, it should be the last. I have hit dogs in the face, but it was when I had 120lbs of German Shepherd (that cull from above) hanging onto my knee when he snapped. A puppy nipping at my hands? I'll try the yelp and walk away method first, then the mouth grab, and very last a smack. Slow escalation of punishment is the way to retrain this type of behavior most effectively. Smacking has it's place, but it's not the first thing that should be tried. ETA - I have NEVER had to move beyond the mouth grab and I've only had to use that with the really obnoxious pups.
If we want to apply it to horses, think about all the little body signals a horse gives before punishing an unruly colt. Their very first reaction is not to go after the colt with intent to hurt. There is loads of body language that occurs first and then they are usually chased off with threatening behavior, if (and only if) they don't move fast enough (which shows their submissiveness) are they bitten or kicked.
In just about every healthy animal-animal interaction there is a slow escalation of behavior. It is very rare that there is a jump straight to the physical in an "aggressive" manner. It just makes sense to consider that when you are training an animal. Just like riding. When you're teaching a horse to yield to your leg, do you give a ton of pressure before it even understands? Or to you begin softly and teach?
This is a similar situation. This pup doesn't understand that what she is doing is wrong because she has never been taught. She has to be taught what is appropriate and the best way to do it is to use a language she understands.