This TIME headline seems totally disconnected from the article, which is about COX-2 inhibitors.
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.)
http://www.nejm.org/doi/full/10.1056/NEJMoa1611593
The paper draws no conclusions about the relative safety of ibuprofen. The only claim is that celecoxib is not inferior to the other two NSAIDs.
Note that this research study was funded by Pfizer, the company that markets Celebrex.
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.
FYI, celecoxib is the generic name for Celebrex.