Actually, my intent was just the opposite: to explain why Google "needs" social (but not so much to explain why its efforts have been weak). That said, I think it does offer explanation for their weakness in social to date: they didn't really see it as a threat until it became one. It's very easy to see why Facebook's ad platform can be a threat to Google's ad platform in hindsight (i.e., right now), but it wasn't back when Facebook was first taking off. It's hard to blame Google for not seeing Facebook as an existential threat before it turned into one.

"Say Google is approaching social as an information gathering problem, and Facebook is approaching social as a users-interacting problem, then who will always win social under those conditions?"

For Google, it's not about winning social, per se; it's about winning advertising. Facebook is trying to win social. Google is trying to prevent social from devastating its ad platform, and at the moment, it seems to think that putting up a valiant fight to carve out a piece of social is the best solution to that problem. That's why Google thinks it "needs" social. It may or may not actually need to win social, but it needs to defend and improve its ad platform, and social is a big threat to that platform. Accordingly, I'd argue that Google's approach to social has been defensive, and not offensive. (Ironically, that may also explain its not being able to "get" social so far).