The first and third tiers (elimination and controls) are the same thing: separating the hazard from potential injury conditions. This can be spatial separation, temporal separation, or a dozen other kinds. A real-world example is how xray techs have to physically leave the exposure area and stand behind a lead panel to turn on the beam. The hazard (radiation exposure) remains, but the system is safe because the tech can't be exposed to it. We use this all the time in software. Process boundaries are a form of spatial separation, mutexes enforce temporal separation. test/prod systems, principle of least privilege, separation of concerns, etc.
Elimination is completely getting rid of the hazard. (In the case of x-ray it would be just not doing an x-ray at all)
Instead, the author says "we could eliminate the production environment or we could eliminate the database" which really makes no sense.