That's not what Twitter is doing. If that was their goal they'd be suing Gawker and TMZ.
The point isn't to stop deleted tweets from being disseminated at all - that's impossible and I'm sure they're smart enough to know that.
The sole purpose of sites like Politwoops was to undo a feature of Twitter's product. Not only that, but they were using Twitter's own API to accomplish that. Twitter's goal is to set the precedent that that's not ok.