Looking at the evidence, it appears it was more a case of -suggesting- it was false, rather than outright saying it was. The U.S. government funded NPR news outlet certainly suggested this in the following article shortly after the New York Post article came out:
Analysis: Questionable 'N.Y. Post' Scoop Driven By Ex-Hannity Producer And Giuliani | NPR
I don't know the details yet, but I suspect that, much like Russiagate, it only had the earmarks for those who were eager to believe anything bad about Russia.
I tend to avoid western mainstream news because it is filled with propaganda on the subjects I'm interested in, yes. Right now, those subjects are the Ukraine war and the Covid narrative, more on the former for now. When it comes to the Ukraine war, Russia provides a refreshing take, as it clearly isn't going to peddle on the anti Russian propaganda that nauseates me when I read almost all of the western mainstream media on the subject.
I get more than enough of it when reading their talking points from posters in forums. Scheerpost, which has includes some good journalists who used to write for the mainstream media before they came to believe that it'd become almost hopelessly corrupted, helps greatly in discerning all the propaganda in it as well.