It depends on the context. If you have a dispute with the credit card holder, you are responsible to him/her for reimbursement of the cost. If you have a dispute with the seller, you purchased the item because you were an authorized user of the credit card. The seller can see your face on the security video etc. However, if the credit card holder told you to purchase the item for him/her using his/her credit card but you physically purchased the item, then the credit card holder is the purchaser and you were the agent.

Ordinarily, in a simple everyday transaction, the buyer is the person who selects the merchandise, then stands in front of the merchant and agrees to purchase and pay for the item, and the payment is presumed to be made by or on behalf of that person. However, as Mr. Cohen has pointed out, there may also be a separate agency agreement - express or implied - between the person who deals face-to-face with the seller, and some third person.

For example, 40 or 50 years ago, my father might have given me a quarter and told me to run down to the corner store and buy him a pack of Lucky Strikes. The cigarettes would belong to him, because I was his agent.

Here, what you bought with the borrowed (?) credit card is yours, unless you and a third party had agreed that you were running this errand as the third party's agent. If the cardholder didn't intend to make a gift to you, you probably need to reimburse the cardholder.

The buyer, through potential criminal fraud if done without the consent of the card holder.