I was still having problems, but this worked for me:
QUICK:
In iTunes, go into Account Info/Payment Info and select None. Save that, then logout, go to the apple store on the web, login and enter your credit card details. Save it and you should be right to purchase things on the AppleTV.
STEP BY STEP:
1) on you computer, load up iTunes and click on iTunes Store in the right column
2) click Account on the Quick Links menu on the right of the iTunes Store window (sign in if you need to)
3) under the heading Apple ID Summary the second option down is Payment Information. Click Edit > to the right of it
4) click None as your payment method
5) scroll down the page and click "Done"
6) go to the store menu at the top of the screen and select the menu item Sign Out
7) open a web browser and go to store.apple.com DO NOT FORGET TO ADD YOUR COUNTRY CODE IF YOU ARE NOT IN THE US (eg: I am in Australia, so I go to store.apple.com.au )
8) click the Account link near the top right hand part of the store web page
9) select Account Home page
10) click Change your default shipping or billing info
11) login using your appleid and password
12) in the payment information section click the Edit button
13) the payment information should be blank (we cleared it in step 4)
14) enter your card number, expiry date and security code (you don't need to change billing address)
15) click save
This should get your account payment information reset. To be sure, log out of your account on the AppleTV (go to Settings->General->iTunes Store and logout). Then go try your purchase. If you are asked to verify your purchase by entering your credit card number, don't bother: if this has worked you will not be prompted for anything.
This worked for me (AppleTV 3, just bought today, Dec 2, 2012) .