It found no strong evidence of any association for acetaminophen, but the 95% confidence interval on the result is pretty wide. So it doesn't entirely rule out the possibility of there being a relationship, and based on its results alone it's entirely plausible that a test with more statistical power could find that it doubles your risk of Alzheimer's disease. But it could also plausibly find that it has a mild protective effect.
Regardless of which is the case, this study still strongly challenges what's being suggested by TFA. Even a doubling of Alzheimer's risk resulting from a lifetime of acetaminophen use is nothing at all like its suggestion that Alzheimer's is a disease that was unheard of before the development of NSAIDs related to Tylenol.
Minor point: Tylenol isn't an NSAID, nor is the prior drug to which the article links Alzheimer's.
"In addition, we examined use of acetaminophen...No association was found between AD risk and use of acetaminophen"
How do you think 25cf should have handled this differently?
If you're misunderstanding something, don't worry, someone will set you straight.