Those of us that are in 'sales' and most webdevs are, to some degree, even those with straight info sites, come to understand that disagreeing with a person's beliefs, mental models, what have you on a subject is the quickest way to lose a customer/sale. How to overcome that 'wall' by various subversive methodologies is both an art and a science.
I've watched and listened while great salespeople (I'm not one) gently lead by agreeing until white is accepted as black (that's a metaphor for a 180 flip in belief, OK?) or vice versa. Or, in instances where the belief will not be modified accept the salesperson as worth recommending as a person even if not the product/service. Truly fascinating.
Recently, with the increase in 'fake news', particularly in politics, there is a spillover in the spread of false product/service information; it's no longer just making connections with visitors different mental models aka their understanding of your niche/subject (broad) and brand/product/service (narrow) to make desired conversions but increasingly also playing defence against some meme or other spread of false or misleading information and the corresponding shift in visitors' beliefs on the subject.
Occasionally the fake news actually makes whatever look good. In the long run this is likely to bite back with uncertain results. Usually, however, the effect is bad; as the cliché: good is spread one to one, bad one to many.
Over the years I've responded to various 'real news' effects in my niches: tampered or contaminated products, restrictive regulation changes, etc. Generally truth will out and being upfront and sharing all available factual information (albeit framed within a preferred storyline - it's marketing after all) is sufficient. Indeed it is a fabulous method for link acquisition. 'Real news' is, more often than not, off to the side as it were of visitors' mental models. Regulation change tends to have more chance of decided views (i.e. for or against), here it is more a matter of being helpful without stepping too hard on anyone's toes while still telling the story to make your points, tell your truth.
'Fake news' is different. It 'infects' it's targets while being dismissed out of hand by those whose current subject view is sufficiently other. Those who accept the fake as real have their mental model immediately changed to incorporate it. Even when presented with the 'real' most will resist accepting their adjusted model as wrong.
Fact checking is all the rage in politics; yet the 'truth' rarely seems to set anyone free. Similarly in our corner of web commerce. What seems to work best - should fake news hit your niche/product/service - is twofold:
Have covered the topic sufficiently, both in breadth and depth, that the 'fake' has no real opening to latch onto, no edge to take on a tangent. While this will have little/no effect on the wider web it may well have inoculated prior/regular site visitors such that they can tell their family and friends the hooey is just that.
It also can be a good source of back links should fact checkers or commentators be looking for ammunition in response.
Don't respond with the 'facts'. Don't be aggressive in response. The fake news cancer has shifted the targets' understanding of the issue; people tend to respond 'hard' to being told they are wrong.
Respond with questions. Build a responsive narrative. Be subtle. Be truthful (which is subtly different from merely factual).
Will you change their minds? A few, maybe. Regardless, you can not just ignore the misinformation on the basis that it is false because that means ignoring the people who have heard it and worse those who will help spread it. Containment is good.
If you have a marketing presence on SM gently use it to leverage your response questions - dialogue is good. People are tribal and if their group begins to question so may they. Remember that typically fake news affects a minority, 'use' the majority (softly, softly) to run with your questions and pressure reversion from the 'wrong'.
Note: sometimes a meme can have it's perspective shifted. Personally I detest memes, however they do make good broadcast (inoculation) channels. If one is very very careful.
Marketing, for those of us that engage in it is ever interesting (as in the Chinese curse).