I can't speak for Time, which has gone through a lot of ownership travails recently (albeit not as dire as Newsweek), but there are certainly still magazines and newspapers that do fact-checking. Some have full-time fact checking departments; the New Yorker in specific and Condé Nast publications in general are historically known for that. Newspapers may not employ people with the title of "fact checker" (although the New York Times has at least one staff reporter who does, in fact, have that title, Linda Qiu), but it's something that's generally the job of the editorial staff to do fact-checking.

Sure, newspapers fail at this occasionally, especially with articles that get rushed due to timeliness -- and unless it's a big long-form investigative journalism piece, it's quite likely only what editors consider the major elements have been vetted. (The old saw "if the paper got this small detail wrong, how can I trust them on the big claims they're making" largely has it backward: the big claims are the ones they want receipts for, whereas the small details are more likely to get passed through without due checking. This is, at the least, what I was told by a newspaper editor many years ago!)