When you opened the account at Blockbuster, you probably secured your account using a credit card. That means that you signed a paper agreeing to let them charge your credit card if you didn’t return the movie. So, yes, they can do that, even after you canceled the card. Otherwise one could rent a car with a credit card, cancel the card immediately after leaving the office, then drive off with the car, never to return, and then think that the rental car agency would have no recourse. Trust me, your card would be charged.
I just canceled my Discover card because I never used it. I got a letter from them saying that they canceled my account, but if anyone attempted to use it within the next 6 months, they would consider that as a request to re-open the account, complete with a new, crappy interest rate. They also stipulated that I should notify anyone I had pre-authorized to charge that account, such as BillPays, etc., of the cancellation.
Pbzep, quit wasting your valuable time calling the credit card company and arguing with them. I had similar trouble with one vendor and after a lot of aggravation and time, I got smart and called the Online Banking specialists at my bank. I explained the situation to the agent and she took it from there. Lo and behold!, the vendor never again charged me another erroneous late fee.