bocadillo
Water Gypsy
How could a payment be processed through a POS terminal if the card number is no longer valid
I have no idea of the processes that are gone through, but there are lots of examples quoted on the net from people who have been charged even after they have cancelled their cards or changed their account numbers. There are hundreds of examples of people who have been committed to CPAs who have felt safe "because they are like a Direct Debit" and who have found out later, to the their cost, just how different the two payment systems are.
And it's very odd that the companies who use CPAs rather than DDs are the ones who people regard as unscrupulous. If somebody on the telephone tells you that a CPA is just like a DD, the best course of action is to say, "No, it's not", and to put the phone down. The very mention of a Continuous Payment Authority should set the alarm bells ringing.