This is what's called psychological reactance, a human trait that means once people are aware something is being kept from them, their motivation to access and spread the information is increased. Reactances can occur when someone is heavily pressured to accept a certain view or attitude. Reactance can cause the person to adopt or strengthen a view or attitude that is contrary to what was intended, and also increases resistance to persuasion. People using reverse psychology are playing on at least an informal awareness of reactance, attempting to influence someone to choose the opposite of what they request.
Apply that principle to social media and you begin to understand the nature of certain fandoms, the vehemence of many political supporters and to a certain extent why some content ends up going viral, despite it being fairly straight forward or even boring. Used cleverly, it also ensures that be feigning modesty and giving the impression that you're trying to avoid attention to certain content, is almost guaranteed to ensure that it actually gains more attention than it would have ordinarily. So for example, an article using a title along the lines of "We reveal the images they didn't want you to see" straightaway creates a curiousity in the reader, making them want to see what they're not supposed to.
The best example I can give you has been dubbed 'The Streisand Effect' by Mike Masnick of TechDirt. It is named after American entertainer Barbara Streisand, whose 2003 attempt to suppress photographs of her residence in Malibu, California inadvertently drew further public attention to it. The $50 million lawsuit endeavoured to remove an aerial photograph of Streisand's mansion from the publicly available collection of 12,000 California coastline photographs. The beachfront property had been photographed innocently, to document coastal erosion as part of the California Coastal Records Project, which was intended to influence government policymakers.
Before Streisand filed her lawsuit, 'Image 3850' as it was known in the archive, had been downloaded from the website only six times; two of those downloads were by Streisand's attorneys. However, as a result of the case, public knowledge of the picture increased substantially and more than 420,000 people viewed the photo over the following month. Naturally, when word spread across social media, more and more people viewed the photo, drawing far more attention to it, simply as a result of trying to have it removed.
In 2015 the phenomena was famously proved once more, when Tinder publicly criticised a journalist on Twitter for an article and survey in Vanity Fair about the 'hooking-up' culture she felt it promoted. There were over 30 tweets in the barrage, some with reasonable points but some with strange pretensions towards Tinder being a force of freedom and social justice in the more troubled parts of the world. Again, as a perfect example of psychological reactance, had they simply ignored the article it may have passed without incident. However, by calling it out on Twitter they effectively gave it a larger audience than it's initial circulation.
The majority of cases we've seen over recent years have had a negative effect on brands, through social media, like Tinder experienced in 2015. But there are brands using versions of it in their marketing already to great success. We know that perceived loss or missing out is a greater trigger for sales than simply telling people that something is available to buy. Just think about it, you've probably seen it already without realising it.
Knowing your audience is the key to social media. Knowing how humans react to certain situations, content and wording can give you a massive edge over your competitors.