The problem is stories taken out of context via Facebook-sharing etc
For a story by itself, I imagine there's a sliding scale something like this:
1. Factually truthful, substantially impartial
2. True, though incomplete facts, partisan narrative
3. Facts substantially "selected" or quoted out of context in order to push a narrative
4. Partisan conjecture quoted, implicitly as "fact" to stir emotive response and 'shares'
5. Blatent lies / BS written either to advocate a cause/political viewpoint/stir up hatred and/or written for the primary purpose of generating 'shares', clickbait and ad-revenue.
If you read many stories from a particular news source regularly, it becomes pretty obvious where a publication is coming from. Even if the site is primarily in the (1) (2) categories, it may have "Opinion/Comment" or "Satire" sections where the journalistic constraints are more relaxed - but you soon recognise them.
Plenty of people will take a regular look at newsthump, thedailymash, thepoke sites etc - and that's fairly harmless - you know the site and know it's just for a laugh - and those sites are fairly up-front about what they are.
Problems arise when individual stories are "deep-linked" through "shares" on social media, and where many will "share" having only seen the headline and image, without even having read it, and when those stories are published by overseas media (that may be mainstream, biased, or just someone in their bedroom) - that the readers are not familiar with.
You can argue that any publication or media funded substantially by advertisements is, taken to its logical conclusion, a business of generating the cheapest content that draws a large number of eyeballs in order to 'hang' advertisements off of. It has probably been ever thus, since the dawn of commercial TV, and before that. A difference is that now anyone can publish and set up online ads (via Google AdSense etc) the lowest-common-denominator model is accessible to anyone who wants to make a fast buck.
The 'problem' of "fake news" is likely more a symptom of the social-media ecosystem, short-attention-spans, sites funded by easy ad-revenue, than a 'problem' worth trying to tackle or legislate for in its own right.
We suspect that Facebook and their ilk internally relate "importance" of a story or link (and thus the likelihood to show it to others) to number-of-shares - which inherently causes clickbaity or emotive rubbish to accelerate to the top of the pile. I reckon the 'problem' is substantially tied to Facebook's model.
I'm unconvinced about employing a select band of "fact checkers" (besides the case that they're likely having to rely on other second- or third-hand sources and "reputation")... fully-spurious fake news can generated far faster than anyone can check it. It's the same problem scientists have with trying to refute pseudo-science - it tires you out, totally wastes your time, and you can never beat it.