Why does iTunes ask me to verify an email account that's already verified?
Well, I haven't figured out what was causing the problem, but did find a way to solve it:


Go to the my account page for your Apple ID Account and click "Change Account Information".
Change your email address from the one you want to use to any other address (to be safe, it's probably preferable to use one you can access, but it's not crucial, as long as you can remember it easily, because you're going to change it right back.
Once it confirms that it's changed it, go right back in and change it back to the one you started with.


This will essentially "clear" the previous verification for the address, eliminating the disconnect where itunes wants you to verify, but you can't, because all the other apple clients know that you already have.  You'll get a fresh verification email, and (at least in my case) you'll be back in business.