Google hasn't given up on its plans to add social features to its products, in fact it's going all or nothing with Google Me, and is now introducing a new feature to Google News, a top of the most shared stories of the moment. It's not clear if this is part of the broader strategy at Google, but the new feature is a perfect fit for News, even though it not exactly front and center at the moment.
The Most Shared section in Google News, as the name implies, displays the most popular stories of the moment based on how many people are sharing them. At this point it's unclear what sources Google is using, though it seems to aggregate several.
Google has a deal with Twitter for full access to the "fire hose," the complete data stream on the microbloggin site. It does seem that Google is using this data stream to determine which are the most shared news stories. It could also be relying on its own data from the Google Toolbar for example.
The Most Shared section is rather buried at this point and you have to scroll down on the Google News homepage quite a bit to get to it. The most likely reason for this is that Google is just testing out the feature for now and doesn't want it to be too prominent before it can get a feel on how people are receiving it.
The popularity of a news story on social networks, Twitter in particular, is certainly relevant and provides an alternative view point to the algoritm-based ranking on Google News.
A hybrid approach is probably the best one, especially for a large portal like Google News, enabling users to find news stories that may be interesting to them from different perspectives. Most likely, Google will continue to experiment with the Most Shared box after this first iteration.