Your problem is that you're interpreting it in terms of "is wrong/is right" instead of "deliberately lying/trying to be accurate". Perhaps news publications should've been more skeptical, but they themselves weren't trying to make things up.
Officials supplied the false information which served as the raw material the media's fake news was produced with.
This is a famous quote from Judith Miller and Michael Gordon, from an article that includes many hawkish quotes from anonymous sources.
"Mr. Hussein's dogged insistence on pursuing his nuclear ambitions, along with what defectors described in interviews as Iraq's push to improve and expand Baghdad's chemical and biological arsenals, have brought Iraq and the United States to the brink of war."
http://www.nytimes.com/2002/09/08/world/threats-responses-ir...
Here's a quote from an opinion piece by William Safire:
"Two terrorist-sponsoring nations are racing to acquire nuclear weapons. One is Iraq, whose scientists already have the know-how..."
http://www.nytimes.com/2002/01/10/opinion/arafat-s-implausib...
Is this fake news? I'd say so. But, I have an even lesser criterion for fake news -- I think the most insidious type of fake news doesn't necessarily tell a single lie, but rather selectively reports the truth.
I am also 100% certain that it's impossible to filter out "fake news", whatever your definition is, without suppressing some true but fringe information.
The politicians involved knew that their claims were not backed up by facts.
They arguably should have been more skeptical but it's very different from the situation where some place like Breitbart runs a propaganda piece which is easily debunked using public information, like the fake electoral map they printed which flipped entire states to maintain the “coastal elites” narrative they're selling.
The mainstream media has some serious blemishes from that era (Valerie Plame comes to mind) but they have editors, publish corrections, etc. and it's a monstrous exaggeration to try to equate the two.
The paid protesters story is a great example: the campaign benefited from and recirculated rumors about that which started on random blogs, conspiracy sites like InfoWars, and outright fakes like abcnews.com.co throughout the election. The guy who tweeted that photo might have been a Republican acting in what he believed was good faith but he was primed to think of that as likely by the prior months of unfounded accusations and as soon as he shared that photo, it was widely circulated by supporters including Corey Lewandowski, who was Trump's campaign manager before becoming CNN's commenter representing the campaign.
Plus, is it really a good idea to suppress a meta-discussion about propaganda and false information? Those "fake news" articles and their corresponding beliefs will still exist, even if Facebook manages to filter them out, but proponents of those ideas will either never see critical discussion or they'll just move to other platforms. It seems like a great way to further fracture our already divided society.