It seems this system uses your scheme, except that instead of getting the key from administrator input, it computes it from the first K passwords it gets using a secret sharing scheme.

The advantage is that the administrator doesn't need to manually intervene, the disadvantage is that you can't verify passwords (in a way that is more secure than just verifying hashes) until you get at least K correct login attempts.

If the goal is only to defend against SQL injection, a much simpler solution is to just put the key outside the database, for instance in the configuration or source of the application.