These people never tell the full stories in their posts. While they haven't done it in a while, Riot has filled in the blanks in the past, and these people are invariably horribly bad ragers, flamers, leavers, or what have you. My favorite was the guy that raged endlessly at someone he knew was a dev, got banned, then made a thread saying he was banned for playing better than the red. He acted like the underdog and got a lot of support before the devs started posting screenshots and chat logs.
On the flip side, mistakes have been made. People have been banned by mistake, but the people where unbanned after talking to Riot about it. Unless you're violating the rules, they'll listen.
Finally, every permaban is reviewed by multiple people. If someone is permabanned, then they really deserved it.