If I'm clicking around on a website and find a gallery of images, that's something I'm supposed to have access to. If I start typing in URLs that aren't linked anywhere on the site, then I'm accessing stuff the site hasn't explicitly indicated I have access to. If I'm doing this with the intent of getting data and distributing to others, then yeah that would be illegal.

The law allows for someone to exercise judgement. The people who do this are not so coincidentally called Judges. If the 4chan guys had have been white hat and reported the issue to the site owners, then they'd be fine. But it's obvious to anyone their intent was to get private information, they poked around to find some private information, and then distributed that private information to others causing a privacy violation. Yes, it was easier to do than it should have been, but it's obvious they had malicious intent and it's obvious they were accessing information they weren't supposed to access.

A crime being really easy to commit doesn't make it no longer a crime. Many times I've seen things that I could easily steal, but I don't steal things when I have an opportunity to do so because a) stealing is wrong and b) saying "they just left this thing out there in a place anyone could steal it" would not be any kind of legal defense. Simply because you're presented an opportunity to do a crime doesn't mean it's acceptable to do a crime, both legally and morally speaking.