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DSimon comments on Harry Potter and the Methods of Rationality discussion thread - Less Wrong
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I wrote out a long response involving an analogy to a CPU self-test program, but at the end I realised that I had arrived at the same conclusion you stated. :-) So I'm voting you up and wish to extend you an Internet high-five.
However, on this topic, it seems like there's no good approach for handling the scenario where your brain messes with your internal tests in such a way as to point them invariably at a false positive, i.e. anosognosia.
I agree that a good self-test of the sort you describe would reduce the probability for most kinds of anything-goes insanity, but what sort of test could be used to check against the not-insignificant subset of insanity that specifically acts against self-tests and forces them to return false positive at the highest level?
It's always possible to produce insane minds that cannot fix themselves - the interesting question is how big a diff can be bridged at what price. And that's a bit more difficult to answer.
I wonder, however, whether a sufficiently educated anosognosiac could determine that the sources informing them of their paralysis were more reliable than their firsthand observations. It seems unlikely, of course.
The answer appears to be no. There were a few articles in Scientific American: Mind about it a while back. Experiments show that the flaw causing stuff like people denying they can't move their arms is part of their logic processing; they proved this by figuring out they could reset their thinking for a short time, at which point people were able to clearly state that they were paralyzed and they were surprised at their earlier thinking.
After a minute, the effect wore off and the patient returned to an earlier state. So the effect appears to short circuit the decision making process on a hardware level.