Yes, your school psych is right: giftedness can alter the reliability of the testing. With what you described, I'd pursue the question of an autism diagnosis further. Knowing what you're dealing with is important, and you'll have a big job educating your school on how to support your child.
We got our best testing at the autism center of a children's hospital; they had the necessary expertise and experience where others had failed us. The gifted/autism combo is rare enough that not everyone knows what to do with it, how to test for it or how to treat it.
I would want the testing to be done by someone with years of experience with kids with Asperger's and/or high functioning autism; that person would probably be a neuropsych or a developmental pediatrician.
I would also want them to repeat some of the tests the school psych did; even a good school psych doesn't always administer tests correctly. And I would expect them to do at least two three-hour sessions with the child, including social and conversational observation, IQ testing, questionnaires about adaptive behavior and social functioning to parents and teachers, so that they have enough information to make an accurate diagnosis.
Here is another good message and information board: OASIS at MAAP,
http://www.aspergersyndrome.org/ -- there is a lot of help there.
HTH
