When a card is present and is swiped in a machine, all the data is read and, quite often, the merchant is required to enter the last 4 digits to ensure that the data is read from the correct card.
When the card is not present and the numbers are provided without visual verification, the security code demonstrates that the buyer has the card in his possession. Additional data such as the numbers of the buyers address and zip code are normally entered to confirm the legitimacy of the transaction.
Providing the security code is not compromising your own security but it is instrumental in confirming that you are in possession of the card.
Milt Sparks reputation goes back a long way and I cannot think of any reason why you should not trust a reputable company.