The truth is this shit works.
It doesn't work on every individual, and it doesn't win every campaign, but there should be no question that it can shape public opinion.
If it didn't work, how could Facebook charge $75 billion a year for it?
Just because something is the status quo doesn't imply that the it is the optimized reality. I work in data science and quite a bit with marketing data, and in my experience, its highly ineffective most of the time. More surprising to though, is the sheer number of people, companies, and dollars, on both sides of the marketing business, with major investments in the idea of marketing being effective.
People believing it works and failing to verify?
Having worked with this technology, I question its effectiveness. Do you have any data to back up your claim that it can sway people's opinion? It seems dubious that it's more effective than traditional brand building through mass media advertising (which itself has never proven to be particularly effective).