I was ripped off for $1400 from three fraudulent credit card transactions back in January. In each case the thief had the correct information: card holder name, address, phone number. In two of the cases the thief put a shipping address that was different than the billing address. I'll usually do some checking if there's a different shipping address to make sure it has some relationship to the person, ie workplace, relative, etc.
In one of the three, I shipped to the card holder, and the card holder claimed he didn't order the product (and that he was under no obligation to return it). I gave the credit card company all of the info I received, including his IP and the name of his hosting company, his cell phone number and the date and time on which he called me, and the delivery receipt from the post office. The credit card company ruled in my favor.
Some of these people are really sophisticated in their techniques and make it hard to spot fraud. The worst thing is that the credit card companies just don't care. They make money on fraudulent transactions, too.