And that would be why I never do a Cat-III without having confirmed with at least one other system first and at least one identifiable light, also an airport that I've landed at before. And I don't know why the FAA even allows it. 200' feet is far too low to trust to a single signal, especially since your aircraft is still going to be sinking while you reconfigure for go-around. Even in the best case, a 737 is still going to shed 50-100' feet before you can regain any altitude. Which, at a lot of airports, if you happened to be 100' to the side of the runway, might put you face to face with with Ground Traffic Controller.
Personally, I set my own decision height at twice the distance it would take for craft to start climbing again + the height of the tallest object within 3 nmi of the airport and 1 nmi of the approach path.
I may be way over-cautious, but from the years I spent in IT before going into aviation, I can no longer trust singular systems, I know how common things like bugs, faulty assumptions, and shoddy hardware are, and there is no way I'm trusting 300+ lives to the QA process of Honeywell or Rockwell (Although I do have in trust in that it is astronomically rare that they'd both screw up in the exact same way)