There was an actual real-life case that is very similar to the OP’s hypothetical.Instead of the NYTimes, it involved people just a reputable: America’s most well-known reporter, Dan Rather and CBS News.
Remember the scandal over GW Bush and his military service?
Dan Rather and CBS news publicized documents defaming G.W. Bush, at a very sensitive moment during the election campaign.
The documents turned out to be a complete forgery.
Rather and his newsagency did not verify the documents before publishing them.
It’s not quite the same as the OP’s hypothetical about intentional forgery. Dan Rather published the forgery unintentionally, but then continued to insist that the documents were real (until eventually the truth was unavoidable.) So it was a case of complete failure of professional responsibility by a reputable news agency.
The results: Dan Rather resigned in disgrace. CBS news issued an apology. And life went on as usual.