I am talking about the sort of prepaid calling cards that you might buy at a gas station or convenience store. I don't know what would happen if you called their customer service line and asked for the logs of your card...

Do you have a source for this? I would love nothing more than for this to be true but I don't think it is. Could this be industry-specific?

Not sure about his industry but all of our calls are recorded in customer service and your verbal acceptance (allegedly) makes you liable for the debt.