Nah, this is like being the "official office supply store of the Washington Nationals" or the "official decaffeinated soft drink of the Washington Nationals." Living Social probably sees this as a marketing opportunity. The only thing that is different is that the money does not go into the Nats as revenue for the ad which they then kick out; it simply relieves them of an expense. The Nats could have stepped in and said to Living Social, "we'll let you be the official sponsor of Nats post-game metro," but that would be cumbersome because of the contingencies and deposit. Much simpler if the Nats do not take a cut on this.
It would be shocking to me if they hadn't talk to the team in the first place. It's likely their out from Selig's bullcrap.