I had this exact same problem. But unlike what The Director has told you, AppleSupport could not fix the problem for me.
The only way they could get it to work was for me to remember 1 of the 2 security question answers, and I could not. My dilemma started out with a regular Support Handler, and then went all the way up to a Manager. Even she did not know how to fix it. I bet if I had stayed there the problem would have gone even higher in the ranks.
That 10$ is still gathering dust on my Apple ID.
Anyway, Director, I have a question... Mirror glass is green, yes?