I had this happen to me in HKG on a SQ flight to SIN. Luckily I had my Blackberry with me, and I signed into my online banking and physically handed the device to her so she could see my name, address and the card number in my online banking dashboard. It took some pleading, but she eventually issued my BP... it was my idea, so don't expect them to allow this all the time, but if it happens, give it a try.