...but it's obviously a valid code otherwise I wouldn't have been able to install the game.
C.
Not necessarily. I explained in the linked post that there are very many keys that will unlock the game, but most of them would not be accepted into your forum profile.
Because of the way DVDs are mass produced, they are identical and cannot contain a unique key. They accept any key that produces a valid checksum form a specific algorithm.
To explain further:
That is why we insist that users register their keys before we give them much support. That is the only way we can be sure that they have a legal copy of the game.
Access to support is about the only incentive to buy the game rather than download it from a pirate site, or “borrow†it from a friend.
A cynic might say “The more bugs, the betterâ€.