This might be vastly oversimplified but "social media" - e.g. according to Millward Brown's findings on social ROI - seem to work upon loyalty measures. To be more exact: being a fan (or somehow digitally engaged) is correlated with more positive attitudes towards the brand and a larger share of wallet.
This is a typical result for loyalty programs. It suffers from the typical "correlation-criticism" that says that loyal customers are simply extremely overrepresented among participators in a loyalty program. In other words: they probably have been loyal before their participation already. And that's why they participate. In the case of social media this is even more plausible because e.g. becoming a fan on facebook is exactly that: being a fan already and expressing that.
This whole notion of loyalizing the already loyal customers also is the main doubt many marketers have (or should have) when it comes to loyalty as a lever for growth: it doesn't bring you new customers but it also doesn't effect the buying behavior of existing ones much. Why?
(Apart from this being well proven empirically, ...) because when people buy you brand a lot (are loyalists) it's hard to make them buy much more or more often. (They will rather not buy a third house insurance from you, they will not buy a third refrigerator, will probably not wash their cloths more often in order to buy more detergent from the brand they are fans of - simply because there are natural limits for purchase frequency and often also for volume.) This differs from category to category but most often the plans to raise volume or frequency significantly, sustainably and profitably (!) are quite unrealistic. You might argue that cross-selling is generates growth but cross-selling is rather a matter of selling than of emotional brand loyalty and by the way also has natural limits - e.g. through already owning those products from a competitor brand.
Social media - such as facebook sites - are rather loyalty programs than customer acquisition programs and as such they tend not to contribute very much to a brand's growth.
Please read a newer post on how social influence - as opposed to "social media" - can on the contrary be a great force - probably even when it comes to gaining new customers: read it here.