That isn't true either. Amazon, before the agency model was put in place, was using a wholesale model. Amazon would pay the publisher directly a set price per book. The number I generally see is that this price paid to the publisher is 50% of retail. Amazon itself then would set the price of the book being sold. The publisher had no say at all in the price of the book, Amazon did. The problem obviously is that nobody has the leverage that Amazon does and companies like Apple hoping to break into the ebook business had no real incentive to do so. Amazon could and did sell many books at a loss to increase their market share. Regardless the publisher still gets their 50% of retail for each book sold.
In contrast the problem with the agency model is that it easily can lead to collusion and artificially inflated prices. In the agency model the publisher directly sets the prices and they keep 70% of the price with 30% going to the seller. This means that for books to be sold at a discounted price the publisher has to be the one discounting it. Amazon, Apple, etc. have no control over the price of the book in this case. Amazon wants to be able to compete by having better prices. Apple wants to compete by product recognition / brand loyalty.