For online transactions, least in my business, it's not the banks that eat the fraud charges it's the business. If someone uses your card to purchases services, and then later there is a charge back due to you reporting fraud, my business would lose the money that was paid from the card and would be fined $25 dollars. So for example say someone signed up for a VoIP service, made a bunch of calls through that service that were charged. You later check your credit card, see some fraudulent charges and then do a charge back. Well the bank/credit card company gets the money from the VoIP service and fines them.
