Interesting to see your experience as I was searching through threads here regarding a problem I encountered with trying to book and ticket an OZ trip.

Using the flyasiana.com site, I entered all my reservation information, selected seats, got all the way to the end of the process, clicked "Pay" and I received a popup saying that the reservation could not be completed and I must contact a reservations office or the "internet desk". I never got to the point of entering credit card information. There was no contact for the "internet desk", so I called reservations in BKK. As with your experience, they would not accept a credit card by phone and only at their office. Problem is, I am in Chiang Mai. The second suggestion was a bank transfer as archaic as that sounds. I do not maintain a large cash balance in my local account and an international transfer would take days being costly. The third suggestion was to message "Voice of the Customer" from the website, which I did and two days later received a message with the same two payment suggestions. I have flown OZ perhaps ten times in the past and this was never a problem, so I am unclear what the issue is now.

Result: It is impossible to book and pay for a ticket using a credit card either by the OZ website or by phone. What an incredible fail and it beggars belief that a major international airline follows this obtuse payment policy and procedure. I wonder how much revenue they are losing as a result. I can personally vouch for two tickets today in lieu of OZ, for which I booked and paid with ease with NH.