There's that. There's a cultural fear of aspartame that could cause people who don't like their child's diagnose to over report aspartame consumption* because they want something to blame. There's self selection in the study group (235 kids with autism vs 120 without is not a random population sample). I made the quip in another comment this is self reported consumption from memory.

*That 200+ vs 100+ ratio in the groups kinda implies they went looking for this specific connection rather than it just popping up as they did various regressions, and if you're looking for a specific connection it's easy to accidently-on-purpose pull in people who already believe in that connection which can color their recollection.