Just because we know one thing it does doesn't mean we know all the things it does.
And just because one of the things it does is inhibit cyclooxygenase, and another thing it does is relieve pain, doesn't mean that inhibiting cyclooxygenase always relieves pain.
And just because acetominophen does inhibit cyclooxygenase and relieve pain in most people doesn't mean it does that in all people.
And since the placebo effect is a thing, and most people don't take acetominophen while "blinded" as part of a study, and since the placebo effect is particularly strong at pain relief, a lot of the effects of acetominophen itself will often be confounded with placebo effects.
So, we know some ways that acetominophen works. But we're pretty far away from a complete theory of how acetominophen works, because (a) biology is messy, (b) humans even moreso, and (c) we don't have a complete all encompassing theory of general pharmacology to unambiguously map particular molecules to their effects on mammalian bodies anyway.