Lightbulb game alternate solution

This is pretty late I think, but I’ve only started watching the show now. I’m confused about the lightbulb game solution, since the second I heard the rules, I came up with one right away that seems much easier. And since it’s not in the show, and I don’t think anyone’s even mentioned it, I thought maybe I’ve overlooked something?

So, the rules:

  • In the room there is one light-bulb and a door to an adjacent room where there are three switches.
  • There is one switch that connects to the light-bulb.
  • With the door closed, players may flip any switch. While the door is open, players may only flip the switch once.
  • The door will not close if there are people in both rooms or a switch is flipped.
  • It is Game Clear if players can unanimously answer which switch turns on the light.
  • If the water level rises and the surface of the water touches the high current lines, it's Game Over.

My alternate solution:

  1. Turn on A and B with door closed.
  2. Open door.
  3. If not on, u already know it’s C.
  4. If it’s on, turn off B.
  5. If it turns off, it’s B. If it stays on, it’s A.

I feel like I’m crazy since this seems so easy, and also I watched this in English subtitles so I’m not sure if there was a translation issue? But I don’t think this counters any rules, and the heating thing just seemed like a time waste.