When you have a "nuh uh, YOU'RE the one that's fake" situation between two apparently reputable news sources, on a topic with which you have no personal experience or expertise, how are you supposed to figure out which ones are fake?
The instances of so-called "fake news" that I have seen are quite easy for me to "verify" as fake with relative confidence: it's generally an explicitly partisan source with a shady-looking website making an outlandish claim that is not corroborated by any traditional news outlet. The situation you've just described sounds much more difficult for me to verify.
Did you actually read the two articles in question, or did you just look to see whether the sources were "reputable"? In this case, there is a clear discrepancy of facts between the two, and it's not hard to come to an informed opinion. Just read.
Greenwald's fake news is his false description of Eichenwald's reporting. If you read Eichenwald's article, then you have all the "personal experience" you need to see that Greenwald is misrepresenting what he reported. And when you look up Greenwald's past, identical lies, you see that this misinformation campaign is deliberate. It's not a matter of opinion or of trying to judge competing claims. It's laid out right there in front of you if you want to look.
The instances of so-called "fake news" that I have seen are quite easy for me to "verify" as fake with relative confidence: it's generally an explicitly partisan source with a shady-looking website making an outlandish claim that is not corroborated by any traditional news outlet. The situation you've just described sounds much more difficult for me to verify.