If you use your card to make a genuine transaction then almost all of the info needed to make a CNP payment is on the store's copy of the receipt . Extra info sometimes required would be the 3 digit number on the signature strip, your home address and, at best, a password on your card.
If a dishonest person works in the store or rakes through your bins to access a receipt then these payments are possible.
http://tinyurl.com/5fqhu
http://www.cardwatch.org.uk/index.htm (click "card fraud overview")
At the most basic level, if the info supplied (electronically) to your card issuer matches what they have on record (card number, expiry date etc.) then the transaction is immediately approved and assigned an authorisation code which the merchant quotes later to debit the funds. This process is obviously computerised.
Only if there's a suspicious pattern of activity/individual transaction on your card will the transaction either be declined or "referred" for extra security checks (such as the password).
e.g. you use your card, on average, 10 times a month and then suddenly there are loads of payments in a short period of time. In Dollars.
Stopping fraud completely is impossible so if your credit card company are in the process of refunding the money don't continue to be in a mood with them - there's only so much that they (and you) can do.
Is it completely outlandish to think that the average customer would make a payment of �200 over the phone? What checks would you find acceptable if you did try to make a genuine purchase over the phone/internet of �200 before they became intrusive?