I would think it's at least conceivable that the body reacts differently to acetaminophen when it's used to treat pain, versus when it's administered even if the subject is not in pain. And especially since most people take acetaminophen for some pain-relieving purpose, rather than for no purpose at all, I would think it's important to try to emulate those real-world conditions when designing studies like this (although clearly it's difficult to control for something as subjective as pain).
Side note: I absolute hate when articles about scientific studies don't even name the study so you can look it up. In this case, the study appears to be titled "From painkiller to empathy killer: acetaminophen (paracetamol) reduces empathy for pain" and the full text is available here:
https://academic.oup.com/scan/article/11/9/1345/2224135/From...