The point being made is that you are not "narcing to the cops before talking to the other party". The other party is a cop. You are at a massive disadvantage.
I fail to see how the other party having power over you has any bearing on how the situation (beyond setting the norms of how you'd approach them about it or potentially limiting your communication channels to them, which would apply to any topic you approach them about regardless of if you've been wronged).
Not only have you given your boss a chance to compromise your position but you won't have the rapport with their boss that they do. You are just a complaint and until there is a trend of these complaints they most likely will be handwaved away.
Maybe you haven't been through the circlejerk enough but the politics of a place totally shoot down your argument.
Oh, you know throwaway0a5e, they are a troublemaker. I have been trying to deal with some of their performance issues off the book to keep their record clean but you know don't like that and are now calling me out for whatever. You trust me, right boss?
In my opinion, this depends a lot on the severity of the issue anyway. If we're talking about workload assignment or some comments, talking directly will be the best solution. If the issue is serious (sexual harassment, academic fraud etc), directly escalating is warranted.
The only way I can see justifying the "narc first, negotiate later" approach is if I don't expect the "negotiate later" part to ever happen and am simply seeking to be a vindictive jerk and want to cause problems for them.
And it should be obvious, to you, if you do engage in good faith, that the "simply seeking to be a vindictive jerk" is not the reason anyone would have to make this argument.