This is a stupid secret to have been on the final floor.
That was only a secret because he himself misunderstood that the stone was fake, which was never influenced by anyone but him. What would've happened if he never said that the stone was fake? He got to the fifth floor and they said "The stone on the first floor was real" and he would say "Well duh, that's what you told me in the first place. Why would I think it's fake? What kind of secret is that?"
Did they not have a reward planned for the final floor if the person to make it there didn't misunderstand and think the stone was fake?
I don't care how many days or years late it is, or if it' a spoiler from the source material, if someone has the answer to why the Pavilion could've thought that this was a secret to keep for the person to reach the final floor when it was so specific to this exact set of events then please tell me.
The only things that I could think of are that:
A) There was some prophecy/time-travel that foretold that everything would happen this way so it was known he would misunderstand from the start,
B) You could only get to the top floor if you thought the stone was fake,
C) There were different messages depending on what reaction the person who broke the stone had,
D) If the mc hadn't thought the stone was fake the test taker would've said that it was anyway, or the mc was psychically manipulated into thinking the stone was fake.