Have a read on the Lodestone's topic for January 2012:
Prior to Jan 2012 it was indeed only the Japanese that had a direct Credit Card billing method, but that changed about ten months ago.Introducing Easier Payment Methods! (01/26/2012)
In the months leading up to the end of FINAL FANTASY XIV's extended free trial period, we received copious amounts of feedback from customers regarding the billing system. We took that feedback to heart, and have worked to implement new payment options that better meet the needs of our players. As the first step towards our goal, we introduced the ability to utilize additional payment methods to purchase Crysta, and subsequently implemented a system that allowed for the purchase of user-specified amounts of Crysta.
As the next step towards a better customer experience, we are pleased to announce that it is now possible to enter credit/debit card information directly into the system to handle subscription payments. This feature has been by far the most popular request received from the community, and so we are very happy to make it available.
To utilize the new easier-to-use payment options, simply log into the Square Enix Account Management System and select the FINAL FANTASY XIV Service Account to get started.
I'm guessing you haven't logged into the Square Enix Account Management System to check out your payment methods since 2011. This new payment method went live a few weeks AFTER billing started, so if you are unaware of the change, it is because you had a working payment method at the time that allowed your attention to not be drawn to the change.