No, it is the way GP described it. Both transaction fees and reward programs are governed by the same entity: payment processing company. Reward programs were a trick to make people accept high transaction fees, because people fall for the illusion of "getting something in return". In practice, transaction fee is paid by everyone, but many people do not bother to claim their rewards, so it is a net win for payment processors. Also, even people who do claim their rewards usually do not do excesive calculaitons and do not realize that for 3% payment fee they get 0.5-1.5% worth of reward.
Last time I worked at a place that could swipe credit cards, we would get charged one fee for regular cards, and another, much higher fee if it was a rewards card.
(This was back when non-rewards cards were the regular variety, so I'm assuming things have changed since then.)
