This is incorrect, unless they've changed it in the last six months. Earlier this year, I paid using my card while applying my father's companion code to tickets on which he was not a passenger.

They may verify the last name of the cardholder, and they may also require it to be an Alaska Visa, but they don't require the actual card that earned the code to be used for payment.

I agree that the rules make it difficult to game the system, and I'm very glad of that. Allowing the rules to be too easily exploited is a good way to lose the benefit entirely.