At least this worked for me. I just Bought my Apple TV on Friday, and tried now to rent a movie. Got this error message. Going to my MacBook Pro, and I could rent the same movie without doing any updates of the paymentinfo. Either way I did an update as described here:
1) Go to iTunes
2) Go to your account settings (on my version of iTunes, I click my email address in the upper-right)
3) Click the "Edit Payment Information" button
4) Make sure everything is filled out correctly and click "Done"
Restarted the Apple TV box, and it worked!
5) No need to restart AppleTV box, just go to AppleTV Settings and Logout of your account, then login again and it works.
Apple should be using 'push notifications' between its own apps, especially if AppleTV asks you to verify your account; you verify it and then AppleTV never knows about it because it has cached your previous account data that when you try to buy something it doesn't match because, well, you changed/verified your account!. (nice Apple QA team!... Steeeeeve!)
So I had this problem as well. I kept putting the credit card 3 digit code in on iTunes on my pc as requested but to no avail. Then I decided to restart my Apple TV. Not simply put it to sleep but actually power it down. I believe I found this in the settings icon on Apple TV. Anyway, after I did that I went to purchase the movie again and this time Apple TV asked me for the 3 digit code on my credit card. I filled it out and VOILA! It worked! Hope this solution works for others. Glad to help others!