It has nothing to do with them being owned by credit institutions. It is because of national laws and international treaties that they have to cover their asses. Facilitating payment for child pornography, incest, human trafficking, etc., even if it is computer-generated make-believe imagery leaves them open to money laundering charges.
Search for:
"Financial Action Task Force (on Money Laundering)" It was created in the 1980's by the G7
and
"Laundering Sexual Deviance: Targeting Online Pornography through Anti-money Laundering" Proceedings of the 2012 European Intelligence and Security Informatics Conference