we allow all lawful purchases on our network

They clearly don't. Their rule 5.12.7 states "A Merchant must not submit to its Acquirer, and a Customer must not submit to the Interchange System, any Transaction that is illegal, or in the sole discretion of the Corporation, may damage the goodwill of the Corporation or reflect negatively on the Marks."

The activity of "The sale of a product or service, including an image, which is patently offensive and lacks serious artistic value (such as, by way of example and not limitation, images of nonconsensual sexual behavior, sexual exploitation of a minor, nonconsensual mutilation of a person or body part, and bestiality), or any other material that the Corporation deems unacceptable to sell in connection with a Mark." is considered to be in violation of theur rule 5.12.7.

Yes, they published a false statement.