Do many "conspiracy theorists" actually have paranoid schizophrenia?

It seems to me that many seem to have higher than average IQ/intelligence but the part of the mind/brain that puts the information together isn't functioning best which leads to many times they create or adopt conspiracy theories common of paranoid schizophrenia. My grandma is actually an intelligent/articulate elderly woman but my Dad believes told me stories from the past of how she once thought a light in her apartment was a laser spy beam from the government sent to hurt her or something crazy-sounding like that.