Part of the controversy over this question stems from lack of consensus regarding just what a "cure" would look like. Just as there is a spectrum of autism disorders, there's also a spectrum of improved skills and abilities. Some people with autism develop impressive language and social skills -- but still think of themselves as autistic. Are they cured?
Some people with autism are able to be mainstreamed in a typical classroom, make friends and do well but continue to display idiosyncratic speech, self-stimulation and other symptoms of autism. Are they cured?
Bottom line, at this point most mainstream medical practitioners would say there is no cure for autism. But they could be wrong.