Remember spam chain e-mails back in the 0's? There were a lot of stupid viral ideas going around in them, but their reach was rather limited, and they were, generally speaking, not very successful in breaking into the social zeitgeist.
"15 million people liked this" is a lot of social proof. "Uncle Joe + a few dozen other people liked this" is not nearly as much social proof... And viral ideas live and die by the amount of social proof they have.
It's quite possible that what I suggest may not be the best possible fix. In fact, I'll go so far to say that it's not. But I have a hard time imagining that we currently live in the best possible world, such that no amount of tweaking the parameters of these sites will result in improvement. The current outcomes are horrible.