No, it's that the wrong "they" is used.

Interchange goes to issuing banks, not Visa/Mastercard, and that's a big part of why the system is so stable as any competing scheme with a lower interchange will not be offered to customers because it won't be as profitable for the issuers. And, if needed, they can use the whole interchange amount for marketing and cashbacks to make any new scheme uncompetitive, because if it has lower interchange, then it can't match that without losing money.

And the someone that pays is ultimately the consumer. They are the ones all of this is for and produced by.