Same problem just reared its head for me *sigh*. Everything was working fine, including on 2 new iPhone 4Ss, then just today, for seemingly no reason, it started popping up a message on the App Store app that I needed to verify my email. Well I logged in but got the same "Email address is already verified for another Apple ID." message when trying to change it. After a long of painful research I discovered 2 old Apple IDs that I think had my current Apple ID email set as one of the email addresses (why this problem never showed up previously I have no idea).
Since I no longer have the previous email addresses of those, I created 2 temporary email addresses on my own domain to use to temporarily verify the old accounts and free up my current Apple ID from them. That part went fine, I got the emails and clicked on the verification link.
Then the real problems started. I could no longer log into the old Apple IDs using the password which I had just used, apparently the verification process reset the password. OK, so I'll use the "answer security questions" method to log in instead, right? WRONG. For some unfathomable reason, IT CHANGED MY BIRTHDATE. Since birthdate is the first security question, there is no way around this. (And I know my birthday WAS working, because that's how I got into the accounts in the first place, since I didn't have the old email addresses anymore.) And, since the verification process seeminly didn't complete (even though it said it did), I no longer get emails at the new addresses I set up, I assume they reverted back to the old ones, which are forever inaccessible to me!
What a nightmare, and I have a feeling the fix (if there is one) is not going to be an easy one, if the results here are any indication. Apple IDs are a complete and utter mess, and a painful failure seemingly without any resolution! Man, I love Apple products, I've been supporting them for over 20 years and easily 10s of thousands of dollars in purchases, but the whole Apple ID/iCloud ID/Mobile Me ID/iTMS ID fiasco has really soured me and gotten me angry. 😠