No, the point is that when you pay cash, you give more money to the merchant than I do. This enables the merchant to charge me less than they might if all their purchases were by credit card (although not necessarily—I remember reading somewhere that when Wendy's started accepting credit card payment, they saw their average purchase total go up. I know when I published a magazine, the percentage that I paid to the credit card processors for payments was worth the effort of not having to deal with paper checks—taking them to the bank for deposit, having the potential of getting hit with a fee if a check bounced, etc.), so your cash payment is subsidizing my convenience and cash back. The parent comment seemed to imply that the merchant paid a percentage to the credit card companies whether customers paid cash or credit.
But they don't all pay in cash: customer A pays cash, customer B pays with a card that gets 1% cash back, customer C pays with a card that doesn't get cash back. They all buy a $98 item at a retailer.
The credit card company charges 3% in fees, or ~$3 for each of the CC customers, so the retailer is now making $288. So they raise the price of the item to $100. Now all three customers are paying $100 each, the retailer is making $294 again, and the credit card company is making $6. Customer B has a card that gets 1% cash, so they receive $1. Now the net change is:
Now, the way I'm summarizing this situation, is customers A and C have each given $2 to the credit card company, and customer B has given $1 to the credit card company.
You're saying, customers A, B, and C have given $2 to the credit card company, and customer A (the one paying in cash) has given $1 to customer B (the one receiving cash back). That's technically not wrong--it's certainly a way to represent the cash flow that gets you to the same place--but it's a pedantic, inane difference, and it certainly isn't a "correction".
