Need to set AppleID to match iCloud email address

I'm trying to help my mother change her Apple ID from a business email address (she no longer owns the domain for), to match her iCloud email address.

The page http://support.apple.com/kb/ht5622 says that the primary email address and the Apple ID should be the same, and set to your current working email address... but the linked page http://support.apple.com/kb/ht5621 seems to imply that email addresses ending @mac.com, @me.com or @icloud.com are not allowed!

When I go to her account page and edit the AppleID, it seems her icloud address is not allowed. There's a drop-down option to make the IDs the same, and this list contains only the email address she no longer owns, or her icloud address. Selecting the icloud one and pressing submit results in the page refreshing and claiming the details have been change, but they haven't.

What's the solution?