While I'm not sure that Epstein is the best example, US media has certainly been known to indulge in fairly dramatic soft self-censorship. I actually think this is less common than it used to be; the internet breaks it a bit.

A notable case was the unraveling of the whole Iraq WMD story, and especially the yellowcake affair. I suspect that this was notable precisely because well-informed Americans could see BBC et al covering it via the internet while the US media largely ignored it, though; pre-internet cases of media self-censorship would have been far less visible.

In an environment where the Guardian, Daily Mail and various other foreign papers have massive US market penetration via the internet, this sort of thing is probably way less useful; media self-censorship will only be useful for the section of the population who get their news solely from TV (or where the entire global media colludes to censor something, but that seems far less likely).