I really wonder that, because idols have been passed before, right? Like haven't we seen at least one season where someone says like "I want you to hang onto the idol!" and gives it to them...(I guess they would have shown it to us though...)
Jon's exit speech made him sound like he has it with him, though.
Natalie, if she's REALLY smart, will target Keith next, no matter what Jaq wants to do or say. Keith winning F4 immunity is bad - Baylor is going to want the best chance for either her or her mom to win the million. If that means a Keith-Bae-Missy finale, then so be it.
Nat has to play her idol next, so she's guaranteed F4 <3 LOVEEEE this season!!! I also want to comment that Jon appreciated the good move and was a good sport going out. He's going to reel on Missy if she makes F3 though, for the whole trustworthiness speech.
Taking Keith to F3 would be risky for Nat, should she decide to chop either Bay or Missy next (also super unlikely.)