I think it is a current propaganda or messaging strategy: you say “In the uncut recording of the interview, I made really good points, but they spliced it up to make me look stupid,” or “In the uncut version of the interview, my opponent said a bunch of nonsense, but they cut it out.” This works because the broadcaster isn’t going to play the uncut version, and even if they did, nobody would bother watching it.
The broadcaster doesn't need to run the unedited video--anyone can keep a copy. Somebody edits the wrong answer onto a question, produce your unedited recording and point out what they did. (And, in a perfect world, sue for defamation.)