As someone who battles anxiety, depression, and chronic pain (they like to keep each other company), I personally feel the study's utter bullshit.
Tylenol features as a normal part of my day (thank you drug addicts of the world for creating an "opioid problem" and leaving those of us with genuine pain issues out in the cold). I've never noticed any change in mood or lessening of my anxiety.
And Advil (Ibuprofen) is pairs up with the Tylenol, too. Maybe it's different for people's brains that aren't overloaded with pain signals. I remain skeptical.