@Billy Goat Gruff
We're an online retailer of digital cameras and out of 1,000 orders a week, around 100 are fraudulent. Luckily only around 1 every 2 months slip through the net. The ones that do slip through the net, tend to be fraudsters who are able to get access to the credit card holders account and change the registered card address to their own address. This means it passed the address check but we have no way of knowing it's a fraudulent card beyond using our experience to look for certain products / delivery areas which are known to be high risk.
We also allow customer to ship to an address other than the registered card address, as otherwise we'd lose hundreds of orders a week - we perform an additional security check over the phone, which is mildly inconvenient for customers as it can delay the dispatch of the order if they haven't put a contact phone number. However, there is no way round this, give that we are 100% liable.