I don't disagree with your post, but do general Government communiques not come in the form of press releases to all willing outlets?
Perhaps Twitter should at itself to the list, and press releases come with an abridged 280 character surmisal that they could then use.
The government has to fight the meme wars just like anyone else who wants to compete for attention.
Different government agencies and officials at different levels (city, state, national) use all sorts of different communication methods.
Governments have been heavily involved in media campaigns across all channels as long as there's been media.
Press releases are just one communications channel among many. Twitter is just the ~newest in a very long line.