If this is their mission statement they are failing miserably.
They would be succeeding if their mission stated "keeping in touch with friends" or "share cool stuff with friends", which for me is already great.
Of course, when you have a mission statement made by a board, you end with lots of grandiose BS and buzzwords like "open" and "connected".
"Connected" is even more straightforward. Facebook dramatically strengthens weak social ties. I interact with people I never would have kept up with if Facebook didn't exits.
There are plenty of rational criticisms of Facebook, but this isn't one of them.