Imagine if every tweet included info about where to find that users' status messages if Twitter is down. It could simply be the URL of a feed. Unless Twitter went down it would just be stored by your client. But if Twitter should go offline, at least you know how to find out what's going on with at least some of your associates.
It's like having a place to meet your friends after a ballgame, or part of being prepared for an earthquake (I just landed in SF). You arrange for a meeting place if the normal lines of communication go down. You use the normal lines to transmit the place you will be found in cast the line goes down.