Hmm? One of the main results relevant to the wider audience is surely that Ibuprofen no longer looks like the most-recommendable drug because it looks less safe than the alternatives. (Even if some remarks can be made towards the study, that doesn't change the above in terms of presentation and relevance to the audience)
At moderate doses, celecoxib was found to be noninferior to ibuprofen or naproxen with regard to cardiovascular safety. (Funded by Pfizer; ClinicalTrials.gov number, NCT00346216.)
Right, so this mentions ibuprofen explicitly, and it talks about cyclooxygenase-2 selective inhibitors too. I still don't get what your complaint about TIME's title is?
Did you think they should've mentioned celecoxib? That's much less known drug. Mentioning ibuprofen means it's more likely to reach the audience that should care about the study.
Yes, but we don't know whether Pfizer is hiding other similar studies that came to different conclusions. This is a general problem with big pharma research disclosure, not just Pfizer.
The suggestion from the paper (and indeed the body of the article) is that Celecoxib is safer than was being assumed, and very much not that Ibuprofen is more dangerous than was being assumed. In that sense it's a good news article with a bad-news headline needlessly attached.