If that was true then Cambridge Analytica would not make any money. The fact that Cambridge, and facebook, make money, and a ton of it, can make you relatively certain that they can influence people.
That said, plenty of firms make money despite not actually doing as they purport to do. Perhaps Cambridge Analytica and Facebook and the like simply have yet to be exposed as charlatans.
Nobody upthread has disagreed with you on that. So why are you arguing?
Cambridge Analytica might just make money by convincing fools that they have some secret insight or power, when they actually don't. Psychics and mediums have in the past made a ton of money, as did quack doctors. Coca-Cola started out as a quack cure-all and it still makes a ton of money today.
The basic narrative you're pursuing here is one that has cropped up a lot in the past 18 months: voters are, by and large, easily manipulated putty who don't have real reasons or analysis behind their decisions. Instead they simply do whatever shadowy Russian conspirators make them do through subtle manipulation of Facebook, the press, or whatever.
Simple, obvious explanations for what's happening in politics are staring us all straight in the face. Occam's Razor guys ... there is no need to go full chemtrails and pin responsibility on some invisible evidence-free conspiracy of random firms, people and countries. Just assume voters are on average, of average intelligence, and thus probably have reasonably straightforward reasons for doing what they do.