You can't know for sure that this song is about the illuminati. However, I've always thought that this song is talking about authority, and how it changes. Cornell is saying that no matter who runs for office, who takes over authority, the world will always be messed up. The phrase "new damage" is referring to when authority changes, nothing has really changes in the long run and the new leaders are just "new damage" to the world.
You can't know for sure that this song is about the illuminati. However, I've always thought that this song is talking about authority, and how it changes. Cornell is saying that no matter who runs for office, who takes over authority, the world will always be messed up. The phrase "new damage" is referring to when authority changes, nothing has really changes in the long run and the new leaders are just "new damage" to the world.