It’s not super obvious, but although Amazon’s prices were cheaper, the scheme Apple and the publishers came up with allows more freedom for the publishers to set prices. When Amazon was the only game in town they could say “sell your books for this price”. Now they can’t do that.
Amazon was the one doing the “price fixing”, at an artificially low cost. It’s just like one retailer coming in, undercutting the competition, waiting for them to die, and then raising prices. Except that in this case the “competition” is the producers of the books.
Catbertz, the Amazon model required publishers to sell for any price they wanted, as long as that price was no more than $9.99. The Agency model lets the publisher set a price and the retailer gets a flat percentage. It’s basically the same model Apple uses for its app store and that’s been a wild success.
One company cannot "price fix" by itself unless it has a monopoly at some distribution level. If each publisher decided on its own whether to sell or not sell to Amazon based on Amazon's $9.99 maximum pricing model, there would be no problem. If enough of them did that independently and that limited Amazon's supply that would be legal too. The illegality happens when they colluded to lean on Amazon. That hasn't been legal for over a century. The question isn't whether everyone thinks Amazon or Apple has a better pricing model or which is fairer to buyers or even who makes money from it. The collusion was the illegal part.
Apple also stipulated that publishers couldn't let rival retailers sell the same book at a lower price.
Manufacturers setting a minimum retail price walks a very, very fine line based on recent court decisions about whether a manufacturer could limit what price a retailer can sell their product for. A lot of luxury goods manufacturers try to set minimum sale prices to keep the "riff-raff" from selling at a discount. But having one retailer insisting that the manufacturers set a minimum retail price to aim at another retailer's sales method looks pretty illegal to me.
Amazon played tough in the market. Apple and the publishers look like they colluded.