Well, yes, that's the way they did it before computers, but no, the safeguards really weren't there. They used carbon paper to transfer the number from the card to the leaves of the receipt. So when the carbon gets discarded, it becomes trivial for someone downstream of the transaction to pull the carbon out of the trash and use the embedded number to do some internet or telephone-based shopping of his own.

It's funny--29 doesn't sound particularly young, but I'm really suppressing the urge to call you a whippersnapper.