"real" companies that are afraid of this type of fraud should match up the shipping address to the billing address and be done with it. No one is allowed to keep photocopies of other people's cards, through the mail. That's fraud protection for you not them 
The other way to do it is the confirmation number on the back of the card. Maybe this company got burned in the past.
The other way to do it is the confirmation number on the back of the card. Maybe this company got burned in the past.