I have read the numerous posts on this and we're encountering the same stupid error message. We've been trying to buy 800 lousy MS Points and can't because of this Error Mssg, "Your payment instrument could not be authorized. Please contact your provider, or try a different payment option." I took off all my payment options and re-added them. We tried buying the points on the Xbox and my Laptop.
It's bad enough that we can't move the Xbox Live Account to my son's avatar, but now we have to pay $10 to change his gamer tag and can't figure out how to buy points because the site and the Xbox won't take my money to change it.