Again, think back thirty years to a scenario where a politician misspeaks on the news. No network would ever deny a request for a tape or transcript of a news program based solely whether the politician wants his statement to disappear.
Everyone will agree that scraping and highlighting all deleted tweets is distasteful and slimy, but we're talking about politicians here. (Not that they're slimy, but that they exert an undue amount of power over the average bloke. Public interest, democracy, and all that.)