I'm not the person you're replaying to and I don't think that someone should be arrested in the described situation, but I think the logic follows like this.
Police are the people we've put in charge with keeping public order. In the course of that job, they're going to arrest and / or detain people. We want them to always detain the right people, but even a very good police department will detain the wrong people sometimes. So, we give the authority to individual officers to detain people, and we don't second guess their decisions at the time.
Of course, this system only works when there is a functioning review system. Where the policed populace feels like their concerns are listened to by the authority figures. Where officers who misbehave, even by the loose standards of american police, are publicly disciplined. None of these things are common in modern america - but you can still believe in the right for police to detain people and push for better accountability.
I think you should consider how much you are reading into statements before you ascribe particular views to people. You both agree the author was treated deplorably, and you both agree (I assume) that police can do better.
Never is a strong word, though it's pretty close: http://jimfishertruecrime.blogspot.com/2012/01/police-involv... (not a great looking source, but obviously this is not a topic authorities like talking about). In general, I agree with all your points, and I favor a system were non-LEOs investigate LEOs.
"It's rational for officers to arrest law-abiding citizens who are slightly annoying officers."
And I get that a lot of people believe that. But you're wrong. You're so, so wrong.
It saddens me that a lot of cops (like the one in this story) feel as you do, that it's fine for police to grossly abuse their powers.
In a rational world, the cop would no longer be a cop.
In this world, he probably could've raped the kid with a toilet plunger and still remained on the force.