The MC should have picked the demon king reward. Just because you are a traitor doesnt mean you cant be a double traitor. And it would also help eliminate the demon king.
Though in the original timeline, I would think the old #1 would have picked the demon king reward. Not sure about the new one.
There is also a way to cheat the lie detector. For example, ventrilism or having someone look like you.
Lastly, it is also possible no one took the demon king reward, the system is on purpose making them doubt each other. Maybe MC taking no reward is the answer.