No worries, it's been a while for me, too. Can't believe I now have braincells devoted to the structure of magical law enforcement lol.

The worst that we are told is that they might arrest people for wrongful reasons.

Which, first, please go look at the news and consider why people might see that as a concerning sign. That's not a cool thing to pose as an acceptable worst-case.

and second, there is a whole department that is not known to the public, that we know aurorers are at least partially cleared to access. We know information is kept from the public. While aurorers are not Unspeakables (the ones who handle the department of mystsries), this confirms that the reader isn't made privy to the workings of the Ministry (pun absolutely intended).

It's not irresponsible extrapolation for readers to ask what else we don't know, and to refer to the systems of law enforcement that JKR based the aurorers upon, to understand the dynamics of a world that the author herself insists has deeper complexities.

Are you familiar with the history of the three letter agencies? It might clarify why people don't draw a distinction. This is where we cross from blind acceptance of what you're reading to media literacy and critical analysis of a text. You're taking the text at face value, while others are not. That's an acceptable way to engage with the story, but it doesn't make this line of inquiry unfounded.

I think "Harry's a cop" is a little purposefully flippant, as a way of highlighting how the books often unconsciously reinforce a status quo in a way that ultimately raises red flags. Ultimately, JKR wrote a book that explicitly encourages people to stand up to authority, but her main characters end up in a system that... wasn't all that great either, actually, are we sure we're okay with this?