OK let me put it this way: it's not out of the realm of possibility for me that he told the producers in voice-overs or whatever that he planned to look for the idol at camp, and so they put it in a place where he could find it. Because logically what you're saying makes sense but what's logical and what's likely aren't always the same thing. And the fact that this worked out so well for the guy who they clearly want to frame as the SUPER MASTERMINDY VILLAIN YOU MUST WATCH THIS SEASON is way too coincidental.
And this way of course, production can't be held responsible for rigging the game. I believe this is more along the lines of how Survivor and BB producers interfere. Although I wouldn't put it past the producers to be like, "Well if you think it's already here, then sure go ahead and look for it. Start near camp though. Say like...right near that tree. It's easier for the cameras."
You do know that sometimes they actually interrupt the game and tell them to move this way and that way so they can "get the right shots", right? And just as the BB producers can use a simple instruction like "Go to the DR" to manipulate the game, Survivor producers can use the fact that they only have so many cameras and have to follow people everywhere, as a reason to give directions in order to manipulate the game.
Like if two people are going off to have a conversation, production can actually say, "Oh can you two go into the jungle to have that conversation instead of along the beach...say north bound? It's easier for this camera guy to follow you that way." And if while doing just that, those two people happen to overhear an important conversation that two other castaways are already having in the jungle, well then...that works out just fine for the narrative doesn't it?