This assumption is very widespread. After the initial reports of exponential increases in rates of autism came out, several studies were done that tended in part to confirm that increased awareness of the disease may have lead to its increased diagnosis. This never accounted for all of the increase, as I understand the studies. However, and in any case, those studies have in their turn been attacked by yet other studies. I give links to these below. First there are two of the early reports on the increase. Then a study arguing for the increase being due to increased diagnosis followed by refutation studies. Then an unrelated study on the topic, reporting that the cause of increase is not dagnosis or better counting. And then another and later study with refutation.
Autism in the United States: A Perspective. (The link is to a pdf file.)
The changing prevalence of autism in California. Pub Med abstract page, where we can read this: “These data suggest that improvements in detection and changes in diagnosis account for the observed increase in autism.” Published June 2002.
Commentary: Blaxill, Baskin, and Spitzer on Croen et al. (2002), The Changing Prevalence of Autism in California. This is a direct criticism and refutation of the preceding article. A person really has to read these articles and decide for herself. This is difficult for most of us to do. So we rely on our chosen authorities.
Response: A Response to Blaxill, Baskin, and Spitzer on Croen et al. (2002), “The Changing Prevalence of Autism in California” This response to the criticism of the preceding article by Croen and Grether, the authors criticized, is quite admirable. If I read it correctly, the authors concede some of the limitations of their data as alleged by Blaxill et al. and provide newly collected data that (in their words) supports Blaxill! They do this twice and in other cases concede that the data is inconclusive and better studies and more data are needed.
UC Davis M.I.N.D. Institute study shows California's autism increase not due to better counting, diagnosis. “Published in the January 2009 issue of the journal Epidemiology, results from the study also suggest that research should shift from genetics to the host of chemicals and infectious microbes in the environment that are likely at the root of changes in the neurodevelopment of California’s children.”
New report shows increase in special education services for autism partly offset by decrease in services for intellectual disability This link leads to a page with a link to the PubMed abstract page. Published July 2015.
Study Concludes Rise in Autism Not Due to Better Diagnosis. September 2015. Here is a link to the full article. This is by David A. Geier et al. I found the approach highly convincing. The authors look at what we might call the profiles of children with autism, mental retardation and cerebral palsey respectively. The profiles are distinct from each other. Things like male/female ratio, birth weight, age of initial diagnosis, and the APGAR score. If MR and CP children were being diagnosed as autistc in significant numbers, then we would expect their profiles to appear significantly among the autism-diagnosed children. But that is not the case. Notice that the profile components are determined at birth.