I don't find the parent's attitude irrational at all. If police brutality was a rare unicorn-like event, then I could understand your point of view, but it's not. Not even remotely so.

I've been lucky in that my interactions with police have ranged from professionally neutral (mostly traffic cops) to indifferent and bored (cop at a police station clearly not giving two shits that I'd just been mugged). (Of course, me being a white male helps with this "luck".) But the stuff I hear about makes me wonder: if I need the police at any point in time, what are my chances of getting a cop that's helpful vs. one that's on a power trip and wants to fuck with me?

I seriously wonder about that, and I seriously will think twice about calling 911 in an emergency. And that's the problem. It doesn't matter one bit what the percentage is: maybe 0.00001% of cops are bad, and the rest are good. But the perception is that a significant portion of cops are just power-hungry assholes who love being able to strap on a gun and show that they have authority over you. Perception matters more than reality sometimes.