The referenced Daily Beast article is still available online, as is their source, a post by Judicial Watch.
The issue in question was in 2009, when the White House wanted Feinberg to do interviews with the major news networks (ABC, CBS, NBC, and CNN), but excluded Fox News. They originally claimed that this was a mistake, but as the documents obtained by Judicial Watch show, this was done deliberately:
> we'd prefer if you skip Fox please
Regarding the broader claim of hypocrisy and CNN not reacting to the issue:
> [ABC, CBS, NBC, and CNN] unanimously said, instantly, no, that's not gonna fly. Either Fox is in or none of us is doing it" source
Ultimately, Feinberg was available for an interview with Fox News.