If they freeze your account and wait for you to receive a piece of paper, they lose the opportunity to profit from your purchases for the next couple of weeks. If you get pissed off and/or take it as an opportunity to start using another card, they might even lose all of your future purchases.
If they don't freeze your account and end up with fraudulent purchases, they probably won't lose any money anyway -- they can either charge it back to the merchant or have insurance pay for it.
If they don't freeze your account and end up with fraudulent purchases, they probably won't lose any money anyway -- they can either charge it back to the merchant or have insurance pay for it.