alt Hacker NewsA flawless predictor would indicate you’re in a simulation [...]
No, it does not. Replace the human with a computer entering the room, the predictor analyzes the computer and the software running on the computer when it enters. If the decision program does not query a hardware random source or some stray cosmic particle changes the choice, the predictor could perfectly predict the choice just by accurately enough emulating the computer. If the program makes any use of external inputs, say the image from an attached webcam, the predictor also needs to know those inputs well enough. The same could, at least in principle, work for humans.
I agree with you that it doesn't require that you are in a simulation, but a flawless predictor would be a strong indication that a simulation is possible, and that should raise our assumed probability that we're in a simulation.