It would make sense for them to take all cards Especially bank//credit cards! The form you found on that other dudes web site says different though. Have you spoken with him, or is that something you just found doing research?
The problem with taking regular debit and credit cards lies in the expiration of the card. The cardholder would be responsible for updating their card with the insurance company. How many of your clients would you feel you could count on to do that?
That is the very reason that TA/Monumental stopped taking them before.