Government vs. private. A media outlet has a full choice in terms of what they send out. They can self-censor and always have. But the government has no business in telling _all_ media what they can or cannot publish. Fake news at its core is not subjective at all. Is Obama on record anywhere saying "I want to institute sharia law"? No. you can write an opinion piece if you think this is the case or have facts but its not _news_ and should be labeled so.

Reading those "fake" news stories I would say that they don't actually claim that. Now, I am sure there's an exception, but I haven't found one and I've honestly read every article in the first 2 pages of google results for "Obama sharia law".

Most take offence at Obama defending muslims and sharia law, voluntary application of sharia law that is, after Newt Gingrich's call for mass-deportation. They do not claim Obama said anything he didn't say. Obama was very political, leaving out any actual controversial statement.

So I don't think, on the whole, that your statement is fair. These articles mostly lack quality, so they're easy to attack. They're not wrong, in a strict sense. Clickbaity, spammy, unpleasant, even misleading ... yes. Wrong, no.

And I have no trouble whatsoever finding all those properties in articles linked from the homepages of CNN, MSN, ... especially in the business and science sections. And I have to say, I am against Trump, but most of the frontpage stuff I would agree if anyone said half of them were hit pieces.