I had to resort to the same fix because i have a non-email apple ID.
for people that have an @me or @mac userid that is no longer valid as email they are semi-screwed for anybody with NON @me/mac email, they can change their primary ID at well just not to/from @me addresses.
my iTunes appleid is just a word eg. MyName
I have a moble-me account MyName@me.com but that is NOT associated with iTunes, however i use it for iCloud syncing.
I was NOT allowed to combine them (me/mac rules) and i absolutely did NOT want to CHANGE my iTunes UserID and add yet another userID into my iTunes collection (i am at the limit of FIVE per device; if i add one more i can no longer sync my iPad).
Soo.... i added a new email address: myemail+itunes@domain.com as my ONLY email address with my MyName apple ID for iTunes. now my emails go through, my iTunes userID is the same as it ever was, no email associated with it etc.
there is NO real problem with the apple user ID for iTunes/iCloud etc NOT being an active email address it just is a 'handle' just like mine which has no @ in it, obviously not a valid email address. it can 'look' like an email address but not be one (myolddefunctemail@eworld.com) but the primary EMAIL can be myfunctioningemail@gmail.com for example.
i think more problems are just from the fact people made add'l unneessary IDs on the path to discovery.
-awr