The rate of police killings is vastly higher in the US than any other Western country. So something is going on there that is not a universal phenomenon.
Gun violence in the US is the symptom of very deep problems, you can't consider it just by itself while disregarding the societal issues being it.
And despite this, it's continually hammered home into their heads that they have a very, very dangerous job. Yeah, you're correct, it's fear from the lies told to them.