Because getting an intern to hack up a 5 minute Python script to do the same is too much effort? OK maintaining a list of current politicians current Twitter accounts is probably where the work is, but if you are interested in a number of prominent accounts this is not that hard a task.
It's a perl script that can hook into Twitter stream API. Sign up for an account, create an access token for ttytter, start subscribing to politicians, and it will suck down every tweet they make in realtime as they make them. If they make a tweet and delete it 30 seconds later, you'll have captured it. That is why whining about deletability of tweets is pointless, anybody with entry-level Linux skills can monitor thousands of politicians.
Now, you could just archive the tweets internally and reveal them under some other name...
How do archive sites and sites like Storify get away with storing deleted tweets? Storify even lets you repost your stories on Twitter.