And the claim is probably bogus. If it were true, we'd expect other evidence (e.g. https://news.ycombinator.com/item?id=45147119) that hasn't showed up. More likely, it's an artefact of autism diagnosis rates varying in different populations, and maybe something to do with autistic mothers' fucky pain tolerances.

More likely to take painkillers + more likely to get your child assessed for autism = observed (tiny) correlation, even in the absence of any causation.