On one hand, it would seem social media should be the responsibility of the PR firm. After all it's their job to monitor/mold the public perception of the brand, respond to issues/opportunities, liase with the influencers, get "free" mentions, etc.
On the other hand, search firms have a unique ability to leverage the digital channel to mine millions of data points and respond in real-time. And it's our jobs (especially when it comes to SEO) to tap the community to drive traffic to our client's web properties.
The answer here, of course, lies somewhere in the middle but it will be interesting to see how it plays out.