The scammer orders the item, using the billing address of the legitimate owner of the card, but a shipping address that corresponds with a freight forwarding operation. These places offer a US address, but forward the shipments on to various places, including South America, islands in the Caribbean, etc.

Typically, the legit card owner notices the transaction way after it's shipped, and files a chargeback. As with all "card not present" transactions, the shop owner then foots the bill, including a chargeback fee.

It took about 3 times getting burned before we took the time to put some countermeasures in place. The most helpful were geo-ip location for the purchase itself, and a "flag this for review" filter for anything going to the Miami area and/or anything with a longish suite number, keywords (freight, global), etc.

Edit: Worth noting that most credit card fraud solutions I've seen don't have a way to take the shipping address (as opposed to billing address) as part of the data to check. For the type of fraud noted above, it's vital. Geo-ip doesn't work well when the buyer is using a US proxy, or US based accomplice.