How is this any different from talking to oneself in public but believing that one is not mentally ill because a few random people nearby might hear what is said?
Perhaps taken to the extreme, where a person walks around all day spouting nonsensical gibberish to no one in particular may well be a sign of mental illness, but this is very different to what most people seem to be referring to when they think of talking to one's self, and obviously different to what you seem to be referring to, as your question revolves around the idea that people's use of Twitter is potentially just them talking to themselves and why this does not indicate mental illness.
I'm sure there are some out there who do just type nonsensical crap into Twitter all day. It certainly seems to me that a great deal of the content that appears on Twitter is inane in the extreme. But none of this supports the underlying assumption of the meme, which seems to be that talking to one's self in any capacity is straying into the realm of mental illness.
There is a large difference between the symptoms of mental disorder and having an introspective conversation with yourself, some or all of which may be spoken out in an audible manner.
Because the former is a bit nutso whereas the latter is a form of self expression and want of communication, regardless whether there's a recipient or not. The anonymity afforded by Twitter/blogs/websites/whatever to broadcast is what drives people to those products. It's not the same as a random person randomly dialing a single phone number to say the same thing.
A lot of posts on HN go nowhere either. Same for blogs.
I guess we just like talking to ourselves.