What makes you believe that this hypothetical comparison is false?
The problem with traditional advertising is that everyone sees it, regardless of their interest in the subject matter or lack thereof. As an advertiser you have to pay to show your ad to a lot of people who aren't likely to be interested.
What Google and Facebook brought to the game was targeting. If you can target your ads to people who are already interested in that subject -- or even just more likely to be interested than the average person -- then your ads will in fact be more effective dollar per dollar. You avoid paying to show the ad to everyone else who is unlikely to be interested.
Some companies like Coca-Cola engage in brand advertising, where their goal is to build awareness and respect for their brand among everyone in the general population. This kind of advertising has less need for precise targeting. But not all companies need this kind of advertising. Plenty of smaller companies are looking to advertise to people who are likely to want their specific product, whether it's a video game or women's clothing or a product for parents of young children, etc.
To give a made-up example, if you're trying to sell an indie video game, then you'll spend your small advertising budget much more effectively if you target your ads to people who enjoy video games, than if you target the general population. If you're selling a first-person shooter video game, then you'd like to target your ads to people who play first-person shooter video games (and not necessarily target video game players who only play Farmville or Bejeweled).
It's very possible for me to imagine that highly targeted advertising to a segment of people who are interested in a product like that will be 1000 times more effective than traditional advertising that everyone sees. You're paying to show it to far fewer people, and each person is far more likely to act on it.