You are indeed correct, yet differences such as these aren't really taken up by some in the population. A few years ago, if I was in throbbing pain, walking through the pharmacy, I wouldn't really have the time or energy (which is really bad and not thoughtful) to search the back labels or ask a pharmacist on whether I should be taking Ibuprofen or Acetaminophen or a placebo.
The point I was trying (maybe failing) to get at, was these drugs regardless of their chemical makeup, most of the time, some of us don't need them but we take the clutch anyway.
They are pain reliefs, not solutions to whatever the pain was caused by.