Thanks for the research.
That's a fairly good representation of the discussions on the topic -- and if one is not paying close attention, thinks acetaminophen is just another NSAID -- but less effective and recommended.
One of its indications is that it is well-known to be safer and to produce fewer allergic/negative side-effects. Like any product, it doesn't work for everyone -- but if it does, one is in luck because generic Tylenol (acetaminophen) is the cheapest thing one can buy at the discount stores.
If it doesn't work, then one has to proceed up the ladder of risk and cost. But I wouldn't start there.
ASA gets on board quickly, and Acetominophen actually prolongs the pain reducing effects. I am especially fond of Exedrine Migraine in these cases.
I'm not attempting to promote one pain reducing medication over another, but I have found that plain old aspirin, in it's many forms, is still most effective in the majority of the population. Those who cannot tolerate NSAIDS have the option of using acetominophen.