If only one bank location has my signature card, then how can I?
Because ANYONE is allowed to give you money. I, personally, could deposit a check into your account if I knew your account number. Its very common in some countries for people to pay/give money to another person by depositing it direct into their account. Thus, they dont care about checking the signature card when you deposit a check into your account, but you could be anyone, not just the account holder.