I didn't read the article, Are you sure they didn't account for this in the study?
Is it possible that the studies that show flu being a risk factor didn't consider that the real culprit was tylenol?
Fair enough, and I didn't read the study either; just the article.
But here's the abstract, and it doesn't look like they did
http://archpedi.jamanetwork.com/article.aspx?articleid=1833486. To do a study accounting for that, you'd need to have made a regular group taking tylenol and a control group to begin with. It doesn't say they asked the mothers if they had felt sick, but even if they had, you have to imagine the sicker ones would be the ones to take the tylenol and so "switch" groups.
And now that we're making fun of scientists and their futile efforts to quantify inquantifiable things, let's notice that the results were based in part on the kids getting prescriptions for ADHD meds, and mightn't we ask whether mothers who are "quicker" to take medication themselves when feeling slightly ill are also more likely to medicate their children?
Even the authors say not to believe it
http://media.jamanetwork.com/news-item/study-examines-acetaminophen-use-in-pregnancy-child-behavioral-problems/.