Actually both Moffat and Gatiss have been very active in online Doctor Who fandom for years. Even when Moffat was writing for the show he still was very active in the fandom and only when he became show runner did he stop posting. They know how fandoms work probably better than many of the newer fans. They know how to play the fans, and they clearly enjoy doing so.

Like people said Freeman's partner regularly posts on Facebook. And even Cumberbatch knows what fans do. He grew up as the son of two actors; actors who had fans (David Tennant!) come up to them.