Moyer himself may have overstated his case against the network: he said that in response to his request, "a producer had sent him an email specifically asking, 'can we replace the climate change with something else?'" That's not a very forceful denial.
Moyer's climate-change complaint probably wasn't the real provocation. It's more likely Fox News didn't care for Moyer's other disgruntled tweets claiming "Every single segment was anti-Obama agitprop" and "Everyone's in a bubble [at Fox News]".
If you worked at Fox News, these tweets would probably have gotten under your skin, too. Moyer could have shown a little restraint, especially since his tweets didn't exactly tell us anything we didn't already know about the network. His impoliteness, however, is no excuse for siccing the mob on him.
It's one thing to call for communicating en masse to a big organization (Fox News, for instance). It's another to tell your big organization — or the followers of your big organization — to go after one person. That's not cute or funny. That's bullying.
Fox News' encouragement, nay, instigation, of bullying is of a piece with the corrosive resentment it stokes in its audience. Fox wants that audience to feel maligned and victimized. It's the most despicable kind of propagandizing.
Was Fox News genuinely irritated by Moyer's criticism? Did it see an opportunity to whip its audience up, just to keep the outrage simmering? Both? Whatever the reason, its call to action was irresponsible and abusive.
I guess we know how the bully reacts to a little criticism.