The credit card system is not my particular area of expertise, but I do know that there are additional levels of security and verification. In some case, people are asked to give out only the numbers appearing on the back of the card. Occasionally, they are asked to provide the last three digits on the back of the card. In the case of somewhat more delicate transactions, the cardholder may be asked to provide some personal information that he or she shared with the financial institution when applying for the card.
These are merely additional layers of security that the person you are dealing with is relying on.