when we read something on a reputable site, we depend on their reputation. The New York Times, and most newspapers, have standards of journalism that are relatively high. They do not publish hearsay, they do not publish information that can not be verified by two sources. They have a long history of doing that, so their readers have come to TRUST what they read, based on their long and faithful adherence to those standards.
Ocassionaly misinformation does get published, but a legitimate journalistic source will seek that out and print a retraction.
Interpretation is a different story. You ask two Jews their opinions, and you will get at least three opinions. The same can be said of those who interpret the news.
In short, we believe what appear to be facts we read in our newspaper because the journalists and editors have been trustworthy in the past.