Fox News interviewed a family (be sure to read the comments to the post on Tom Naugton’s site), Michael and Tula Larson, and their doctor, Dr. Kenneth Bock, (author of Healing the New Childhood Epidemics: Autism, ADHD, Asthma and Allergies) about Tula’s autism and how it was eliminated with diet. The diet is basically the paleo diet, which you could learn about from such books as Mark Sisson‘s Primal Blueprint, Robb Wolf‘s The Paleo Solution, Nora Gedgaudas‘ Primal Body — Primal Mind, or Dr. Art DeVany‘s New Evolution Diet.
The episode and Dr. Bock are criticized on Media Matters. However, Dr. Ann Childers, among numerous other people, has made observations similar to those of Dr. Bock, and has used diet to treat children with mental health problems, as she discussed in an interview by Jimmy Moore. You could also listen to Nora Gedgaudas discuss how diet has an affect on mental health in some of her radio shows (episodes #29, 33, 39). See also the PBS documentary The Medicated Child (which I have not seen, and so cannot recommend; I am posting it here on the implicit recommendation of Tom Naughton) and read the comments to the post.
I’d tend to think that diet does help; however, we’d have to do the (real, proper, inductive and integrated) science and research the (real, proper, inductive and integrated) science that has already been done. If you look into related issues, you will learn how high-fat diets have been used to help children who are not developing neurologically properly and how ketogenic diets are used to treat cancers and neurological problems.