Apparently, they don't know how to resolve the issue either. Here is the final (of several) responses I received from the "Support Team":
Your request for assistance has reached iTunes Store Customer Support, which answers questions about billing, customer accounts, downloading purchases, and iTunes Store content. Although this team does not offer technical support for Apple TV, I'm happy to guide you to some Apple resources that should help.
You may find the following article helpful:
Apple TV: Basic Troubleshooting
http://support.apple.com/kb/HT1551
You can get lots of useful information on our Apple TV support pages, which are packed with instructions to help you use Apple TV and resolve issues:
http://www.apple.com/support/appletv
In Apple's public discussion forums you can read questions and answers provided by experienced users. You can also post questions of your own. Click the Apple TV folder on the Apple Discussions webpage under Digital Life:
https://discussions.apple.com/community/appletv/appletv
For this issue, you may need to call our AppleCare technical support team. A technical Advisor will be able to tell you about Apple's complimentary and fee-based support. The technical Advisor can also assist you in determining what option might be most helpful to you in this case. To find the appropriate phone number, please visit:
Contacting Apple for support and service
http://support.apple.com/kb/HE57
Another option is to describe your issue on our website. After you have described the issue on our website, you can arrange for an Apple Advisor to call you. You can receive a phone call now or you can make an appointment to have an Apple Advisor call you at a more convenient time. To explore this option, please visit Express Lane:
https://expresslane.apple.com/
Certain Express Lane Support options are only free during your Apple hardware product's complimentary support period or with an AppleCare Protection Plan.
Thank you for choosing the iTunes/Mac App Store. Apple appreciates your business. Take care because in Apple, we care.
Sincerely,
Aloha
iTunes Store/Mac App Store Customer Support