With Groupon currently the poster child for social commerce, there's a lack of true social interactions in the current nascent state of social commerce beyond "sharing" the deal with your buds. The group buying concept is essentially another variation to get folks to buy something in the traditional e-commerce sense.
How do deals become social? To get the consumers to aggregate around group buying offline, there needs to be a relevant community overlay on top of the deals. For example, Japan has a social network of housewives who input the best shopping deals that day manually for the benefit of others in the community. Unlike a one-off Groupon deal, the housewives form a local social network.
What is the appropriate community overlay? People respond to three types of local activities - local real time news, things to do and deals. Provide all of these components to a community in the format of a local media resource, and it will create online/offline activity. Think AOL Patch with a deals system within which communities discuss local retailing just like the Japanese housewives (AOL will figure this out soon enough). Once communities congregate around shopping deals, social commerce indeed can be driven by community conversation. The highest level of trust is cultivated most simply by aggregating local folks who actually know each other.