This is the closest that I have seen to an answer:
<i>Since Bitcoin is a digital bearer instrument, the receiver of a payment does not get any information from the sender that can be used to steal money from the sender in the future, either by that merchant or by a criminal who steals that information from the merchant.</i>
I don't know enough about how the costs of payment fraud breakdown to know what percentage of the administrative costs of the system result from stolen card numbers. I can imagine it being a big percentage, but I can also imagine it being relatively small since solutions to it might be have the same characteristics of scalability as the fraud itself whereas the other failure modes associated with credit card fraud require more comprehensive human involvement both in their perpetration and in their redress.
For the moment then, it looks as if Bitcoin is an improvement to existing costly solutions to the BGP, but not an absolute solution. But that's better than no solution at all, which is how it seemed.