Furthermore those 40% comes from all sorts of papers but all but one was against Trump. Yet he won.
Fake news is only useful to fuel your anger if you have already decided. The reason why people are swing voters is exactly because they weight in many factors not because they let themselves be fooled by fake news IMO.
Furthermore the beauty of networks like Facebook and Twitter is that they are self-correcting. The lie doesn't travel faster than the rebuttal of that lie.
Lastly I am not sure the article has a very clear idea of what actually constitutes a lie since a lot of those lies are really just different interpretation of the same things. And FB is actually quite good at having related articles of something which often will have different views in them.
Facebook is one of the places where you actually meet most people of dissenting views to yours.