No the mistake you've made is thinking that their job is defined or limited by the job description. What police do is violence, and it's not off limits at all because they almost never face consequences for the violence they do.

So regardless of what we say the police should be, or the standard we say they should be held to, in practice they beat up who they want and we let them. We keep paying them to do it and don't stop them from doing it, that makes it their job in a very real way.