I do not believe intelligence is correlated with insanity. The statement itself is a semantic mine field because neither trait is very objective. For the purpose of an argument, I would define insanity as being detached from common physical experience to the point that one is unable to communicate and function within standard societal constructs. Intelligence I would define as the capacity to take ideas and form new relationships and abstractions between them.
My understanding is that studies to date have shown no correlation between high IQ and high rates of mental illness. That is to say, smart kids seem to be just as mentally stable as any other kind of kid. Admittedly I have only taken 2 undergraduate courses in psychology, but that is one fact that they mentioned.
The correlation of intelligence to insanity seems to make a lot of sense intuitively, but I think it is based on stereotypes and superficial understanding rather than any objective analysis. If you think about it, there are several obvious facts that could contribute to this view:
Highly intelligent people are more likely to be historically noted. Not because they were intelligent per se, but because more advances and inventions are made by intelligent people than dumb people. So when we think of famous insane people, they probably tend to be of above-average intelligence just to have done something to get into history books to begin with.
Insane people and highly intelligent people both say incomprehensible things. A well-reasoned statement might seem insane to an individual simply because they lack the facilities to comprehend it. Therefore someone who is insane might appear to act much like someone who is contemplating things that are beyond your current level of understanding and vice versa.
You are more likely to notice someone's intelligence if they behave strangely. Many of the smartest people realize that showing your intelligence can be off-putting, so in order to relate better with others they tailor their conversation to the individual. Insane people presumably have no concept of how their words and actions influence others, so they would make no such attempts (at least not successfully). It's similar to the stereotype that 'nerds' in school are smarter than other people when in fact intelligence has very little correlation to social status. What makes someone a nerd is difficulty or disinterest in playing the complicated social games that define children's society. In other words, it has to do more with where they devote their mental facilities rather than how powerful they are.
I can accept that intelligence is correlated with insanity in so much as insanity is defined in the eyes of the beholder. But in terms of intelligence opening up dangerous mental doors that lead off a precipice into 'madness' where the sufferer loses contact with reality, I emphatically reject that hypothesis. If I had to correlate insanity with something, I would say it has more to do with social difficulties than intelligence.