If you go camping in the woods and are afraid of bears, every shadow looks like a bear and every noise sounds like a bear.
I frequently go camping in the woods, I am terrified of snakes and I agree with your general statement. I will frequently carry a machete for the purpose of separating snakes from their lives. The thing is, I don't go wildly swinging every time I see a branch, twig or something in my peripheral vision move. I stop, quickly but safely move away from the thing that could be a snake and try and figure out what it is. If it is a snake, I then take a split second to assess how much of a threat it is to me and respond accordingly. More often than not, I simply avoid it. That's even knowing those bastards are a lot faster than I am, especially when I am tired.
On one particularly horrific trip, I was on a very narrow ridge line and ran into a rattlesnake (and I didn't have my machete). I spent nearly an hour trying to come up with a plan before deciding that chances were pretty good it didn't want to tangle with me. I had to pass well within striking distance but I moved slowly, carefully and deliberately past it. While not deadly, it was a mix of my worst nightmare and a decent dose of venom in the backwoods. I prepared for the worst but hoped for the best. It didn't want to mess with me and we both went out separate ways, happy that the other was gone.
I am not a professional woodsman, ranger or herpetologist. I do not have any training or experience in dealing with snakes outside of "kill them good" and suck at identifying them. Even with that, I know that if I get jumpy or panic then things are going to get really bad really quick and a good outcome becomes more pure fortune than anything else. I would be shocked to find that police are not trained to stay calm and keep the situation under control.