Eichenwald did not claim that the leaked information was falseWhen I follow a link from Greenwald's piece I see this tweet that was sent by Eichenwald: "Russian gov manipulates email to @johnpodesta. Publishes disinformation. Takes it down. Trump recites false info." https://twitter.com/kurteichenwald/status/785676641880027136
I interpret "manipulates" as claiming that the emails to Podesta were changed by the Russian government before they were passed to Wikileaks. Referring to them as "disinformation" also claims that the contents of the emails have been modified. And I take "recites false info" to be reiterating once again that the emails are not genuine.
From the outside, it certainly seems that Greenwald is justified in saying that Eichenwald claimed that the emails were fake. But apart from reading this quote, I'm not familiar with the details here. Could you be more specific, and specify a exact quote from Greenwald that you feel is deliberately distorted, and a corresponding quote from Eichenwald that shows the undistorted truth?