Peter, I was being pedantic :) We were almost agreeing, but...
I was just clarifying that the credit histories are held by the credit reference agencies rather than the credit card companies. The companies would not associate you with anyone else, your account is your account, nobody else could become liable for your debts.
The credit reference agencies might associate you with someone else which has nothing to do with recovering existing debts, but everything to do with how easy it would be for you to get credit in the future. It would be wise to sever the links with anyone with whom you are associated on the credit reference agencies' records if there is no genuine financial link.