The phrasing for quoting sources is extremely codified, it means the journalists have verified who the sources are (either insider or people with access with insider information).
Sure, if you don't trust anything what's the point. There's a lot of information that relies on anonymous sources and we usually use third party to vet them (otherwise how would they stay anonymous). Without this system we'd be missing out on a lot of things (if only named sources are used, a lot of things would never come out).
(A lot of things break down in society without trust, maybe that's already how the US is? Where I live it is thankfully still somewhat ok)
The Washington Post, The New York Times, The New Republic, The Intercept, Rolling Stone, CBS News, CNN, Newsweek, USA Today, NBC News, Der Spiegel (Germany), The Sunday Times (UK), Daily Mail (UK), Al Jazeera (Qatar), RT (Russia), Xinhua (China), Press TV (Iran), Haaretz (Israel), Le Monde (France), El País (Spain) all have been caught using fake anonymous sources.