Yeah I think we're both talking about the same thing, I just initially worded my assertion poorlySince Xander outright said it was a fake and nobody tried to play it, Jeff wouldn't have had any reason to verify if it was or wasn't. Even if it was real and nobody tried to play it, he wouldn't have had a reason.
Jeff only has to verify an idol's authenticity if someone tries to play it.
I think it would have been a great move he hadn't divulged that the idol was fake and gave it to her, and then she went through the game thinking she had a real idol, only to be told it was fake by Jeff at a later date when she tried to use it
That would have been an all time moment