I think this video had good points, but I really don't think this is a case of intuition vs evidence. I think its a case of how much evidence is enough, really. I'm still finding my own opinion on if kp's a pedo from the logs given, but clearly a creep who should've been removed from the community ages ago. I don't think anyone senses he was a creep until they saw the logs and made their own judgement. That isn't exactly a "gut feeling. "
Honestly, I really think there needs to be more prevention, resources from organizations that specialize in these sort of situations should be included and even mandated in things like applications, for example. If I remember correctly, some of these organizations even offer training on spotting and combating these sorts of child predators, something that maybe admins or anyone whose dealing with these situations should be required to do so. Maybe if they're trained in these sort of situations, they wouldn't exactly need to require "irrefutable evidence" or whatever they believe is enough. You say administration has no true idea what grooming is, but who here actually does?. As far as my interactions with the community is, I think everyone has their own definition. I agree with the opinion, administration isn't doing enough, but not in the sense that they should be banning people without any sort of evidence.
And honestly, this is a more personal opinion, I just don't trust some of the community with the ability to just spread rumors that someone is a pedophile enough till they get banned. If someone can just repeat it again and again till someone they conflict with on this servers get banned, I wouldn't put it past some people.