This, this, and this. ^
It's a game for $1,000,000, where "outwit" is one of the mantras. Many a past winner furthered their game by making up shit. What are Kamilla and Kyle supposed to do, just give up and not actually try to win? Eva and Joe were not going to turn on Shauhin without a really really good reason. And it's not as though Shauhin was a saint in all of this. He proposed getting rid of Eva. Would you rather that she had been voted out? That was the likely outcome if Kyle had been confident of beating Shauhin in the end.
The only thing Kyle and Kamilla made up was the part about the idol.
The one thing I'm struggling with is that Kamilla voted for Mitch. The only reason that makes any sense is if she was worried that she might be getting blindsided, and thought it might be a split vote situation between her and Mitch. That could have screwed up the plan if Joe had not been convinced and voted Mitch instead of Shauhin.