Maybe the reason that debit and credit cards don't see as much fraud is because people are more cautious with them?
Actually those cards see a great deal of fraud. Just ask anyone who deals with online orders for a decent-sized company. Part of the reason they have as much fraud as they do is because people are lax in their use and/or storage, because they know they can just perform a chargeback, or can call up their middleman and (often, not always) have him take care of their problem.
Of course, all of these extra services must be paid for too, whether the cost is upfront or hidden.