Except that salting is only intended to make the use of rainbow tables inefficient. It doesn't add a security benefit beyond making it harder to attack an individual password. In this case, it's more accurate to say that in the compromised password DB scenario, this provides a very weak password as a protection against the main password being converted to effectively being a salt.
Unfortunately, that's not likely to do much if someone has both a compromised hash table and your main password and the simple "horcrux" would rapidly be found by brute force hashing given it is short and rememberable.