It seems that higher sensitivity to pain could be a very plausible cause. I believe there's studies showing lowered (and altered) pain tolerance with autism.
Though I'd expect that if aspirin did have an affect that it'd change the prevalence or severity of autism in children having genes related to autism.
There'd be a first order correction fornthe likelihood that aspirin is causitive by controlling for increased ibuprofen and tylonol usage as well. The second order correction would be whether autistic people were more likely to use aspirin over ibuprofen or tylonol, etc.
Aspirin???!! Its not mentioned in the OP. No one here mentioned it. WTF???!
I'm waiting for someone to blame coffee.
Ugh yeah, s/aspirin/Tylenol/. My brain always wants to call Tylenol and acetaminophen as generic "aspirins" and it's a hard habit to break. Joys of having ADHD I didn't even notice the switch.
Nevertheless, comparing the observed correlations of Tylenol with aspirin and ibuprofen would be the first thing to check. Seems unlikely to me that the OP's suggestion could be controlled for that way. I'll be curious if Kennedy's report checks those basic things.
One important point here is that NSAIDs like aspirin and ibuprofen should be avoided at least in the second half of pregnancy. Acetaminophen is usually the “go to” painkiller for pregnant women, which of course skews the result.