Just a note that some of the original posts are from a long time ago so they may not be seen.
btw, you can have all three. You can have more than 3, although all this varies from individual to individual.
Some people will have attention difficulties or obsessive or compulsive behaviours that may not be diagnosed as disordered = OCD for example.
Some people can also have Asperger's and Tourette's Syndrome and OCD, so they may have tics as well as motor stereotypies or self-stimulatory behaviours. There's also Stereotypic Movement Disorder and that can be confused with tics and TS and the children don't have an ASD.
Asperger's isn't an umbrella diagnosis. Once it becomes an umbrella diagnosis then everyone is in trouble who has comorbid conditions because those comorbid conditions are often the reason for difficulties.
Everyone I know with Asperger's is good at math, but it doesn't mean everyone would be. The same as people I know who have ASD diagnoses are geniuses, but it doesn't mean everyone is a genius.
Who is "this person" and their research? I'd be interested in reading it. Thanks.