This is also wrong in some parts. As a former special education teacher and currently a social worker working with autistic children, I can tell you that most autistic children do not show the "genius" for one or two things. That is a stereotype. What most people are referring to when they speak of this is neither Asperger's or autism, but a related disorder on the PDD spectrum referred to as savant syndrome.
Your description of the difficulties in social functioning for PDD spectrum children was spot on.