In my totally unscientific survey of psychologically disturbed individuals, they seem to always default to a paranoia, where everybody is out to get them.
Why does this seem to be the stock & trade of a disturbed individual? Is the human mind really so prone to paranoia – and why?
Paranoia is a symptom of many different mental illnesses and its also easily developed by the most common mental problem: anxiety. So a lot of anxious people eventually develop some level of paranoia. Unchecked worrying and negative thoughts are pretty common.
I think people are learn very quickly to look for threats to their well-being. If you look at it logically, you’re better off thinking that something safe is dangerous than to think that something dangerous is safe. You can phrase that in terms of natural selection, but you can also watch it happen within a person’s lifetime. If you grab pots off the stove and keep burning yourself, you quickly learn to assume that everything on the stove is hot until proven otherwise.
Throw a little dose of crazy into the mix and you get paranoia pretty easily. 
Perhaps crazy people become paranoid because they have reason to. During your totally unscientific survey of psychologically disturbed individuals, did you take any note on how the people around them dealt with the issue? When a person isn’t quite right in the head, most people’s first instinct is not to be direct. Even if it’s as subtle as an unusual personality which makes them hard to get along with. Out of fear of ‘setting him/her off’ they work around the crazy one, and often coordinate with others in doing so. Everyone will settle on a way of handling the issue, without any input from the problem person him/herself, because, obviously everyone else knows what’s good for him/her better than he/she does. In short, people scheme and plot behind the backs of crazy people. I’m not saying they’re wrong to do so, but if you experienced this to the degree and with the frequency to which ‘crazy people’ do… it’d be even more crazy not to become at least a little paranoid.
Well, I’m not sure worrying that somebody thinks that you’re crazy really qualifies as being paranoid. It’s a legitimate concern if you know that you are “a little off.” On the other hand, people do that sort of thing you describe all the time, even to “normal” people. Though the idea that this sort of thing is discussed often is a little strange, as it’s usually just that people notice that one person is treating a person one way, and just do it because the other is. And a lot of people have the same intrinsic reaction to anything they think is different. Put those together, and it looks like they are scheming behind your back.
In reality, though. Most people don’t bother to take the time to even consciously think about you. That was one thing that took me a while to learn. That, and, even if I’m feeling rotten, most outsiders can’t tell.
(I used to think I might have Aspergers*, but I discovered that I actually read body language and non-verbal cues better than most people. In fact, I probably pay too much attention to it.)
*That and other autistic disorders are the most obvious psychological disorders. As people with these disorders are rarely paranoid, this seems to deny the OP’s claim. I think it’s just more likely that, when we say “crazy”, we just mean paranoid.