It was advantagous for him to issue a public apology but that doesn't mean that the affair damaged him and that he isn't better of them at the start.

I wouldn't regard him as better off, and I have serious doubts he regards himself as better off, but we can disagree there. At any rate, he's not actually a useful counterexample, since he wasn't defending against attacks, but provoking them, and then responding... pretty much exactly according to the script. (Violated the hell out of Rule 1, though.)

People like reading stories that evolve. Journalists like to provide those stories to them. The desire to read how a story progresses makes people buy a new newspaper. With online media it's a bit different but even there jouranlists want to advance stories.

That might have been true twenty years ago. People's attention spans don't support that now. Even when it was true, however, the quick capitulation prevents evolution of the story. That's why that particular rule calls for -immediate- surrender; if you take a week to respond, you're dragging the story out and sustaining interest.

Most of the time the actors in the interaction care but many issues besides the actual conflict.

Yes. That's one of the other critical reasons for immediate capitulation; you prevent your own side from needing to throw in on your side and -create- a controversy. If nobody is arguing about it, everybody's attention moves on.