There are two easy ways to influence the editing when you are being interviewed by a journalist.
Full marks to Gerry Brownlee. The earthquake minister may have his critics, but he knows how to deal with the media when he's made a mistake: front up to the stuff-up. He promised Canterbury that red-zone homeowners would be paid for house improvements - which turned out to be much more than he could deliver. So he went on camera, openly admitted the mistake, expressed regret and apologized.
But to gain more than you lose, it has to be done in a particular way.