I don't think the loser of a callout should have to apologize. That feels way too much like a first grade teacher hauling up a couple squabbling kids by the scruff of their neck and demanding "apologies" which are then given, with zero sincerity, through gritted teeth and with sullen eyes. Only to wait until after school when the kids have at it again with no meddling schoolmarm interference.
There's a certain point of honor in conceding gracefully. But there's also value in standing by your opinions even in the face of intense opposition. A baying crowd is not always right just because they're in the majority. I've seen another callout system where the loser is forbidden from posting again until they apologize to the winner. That's bullshit IMO, and goes against the independent spirit that so many people on the spectrum (and off it) have developed. It's enough of a challenge to stick around and keep your head up after you've taken a hard loss in a callout. I see no reason to drag people through the mud in any kind of forced humiliation.
The dynamics of Scrap's demand are slightly different, because it's hard to imagine the site owner slinking off with his tail between his legs even if he was defeated in a callout. It is, however, easier to imagine his refusing to concede defeat in a draw, and then "winning" by virtue of his position rather than the merits of his argument. Since one of the original points of this callout was the question of whether it was legitimate for Odeon to ban Scrap's sock out of personal vindictiveness rather than an established site rule, I can see how Scrap might believe Odeon might do a similar thing if he got butthurt from losing a callout. I don't personally think Odeon would, but eh, I'm a (relatively) neutral party. Hence Scrap might be asking for the promise of an apology to compensate for the risk of going up against further vindictiveness which he would be powerless to prevent.