I can see this working every time now.
"My credit card was skimmed." "I didn't notice a purchase of $10 to GoDaddy-who would? I haven't balanced a checkbook in over a decade." "I'm more than happy to give up the name, my name already looks bad enough in other places my card was used already!!" <-- feel free to use any one of those convincing arguments with your own twist when caught.