Why? seems reasonable to me. You are liable to the cc. They don't care who got the cash. In the end of the day if he doesn't pay they will come after you. Skipping you in the payment process has no relevance to who the loan is from
The following sounds eminently UNreasonable to me:
You come to me and ask me for a favor, to borrow my cc. I (stupidly?) agree. You spend, say, $1,000. At the end of the month, you don't pay me back contrary to our agreement. I incur fees of $100.
I simply can't get my head around the fact that halacha would dictate that I be responsible for the $100 in interest.
In effect, he is borrowing money from ME, not the CC company, as I would be on the hook as so:
I guess it's the CC AH's liability