Service Charge? I Don't Think So.

CSR: Thank you for calling Capital One customer service, how can I assist you?
DB: Yeah, about a week ago, I called to close my Capital One credit card account, and it seems that you guys have added an annual fee onto the final statement, presumably for the upcoming year that I won't actually be a cardholder.
CSR: Well, it does take 7-10 days for a card cancellation to fully take effect, and any charges during that time period would be valid. I show that your annual renewal date is June 13th, so that would be a valid charge then.
DB: When did I call you to cancel the account?
CSR: I show you having called us on June 10th, sir.
DB: And what day did you charge me for another year of service?
CSR: June 13th.
DB: So, assuming for the moment that I don't care how long it takes you internally to process the closure, because I don't, why would I be willing to pay you a charge for a service I'm not going to partake of, and clearly had no desire to partake of?
CSR: I'm sorry, sir, but that's a valid charge.
DB: May I speak to your supervisor?

SUPE: How can I assist you?
DB: I cancelled my card on June 10th. On June 13th, you decided to charge me for an upcoming year of service that would never happen.
SUPE: Oh, you're right. One sec. *clickety-click* OK, I've made that charge go away, the account should zero itself out and close within the next 24 hours.
DB: Any idea why the CSR I spoke with couldn't do that?
SUPE: They wouldn't?
DB: Nope, gave me some nonsense about how it was valid because a cancellation takes a week or whatever to process, yada yada yada.
SUPE: I'll have a chat with them about that.
DB: Thanks much. Cheers!
SUPE: Have a good day, sir.
DB: You too.

*click*