Didn't you listen to the previous TC? Sierra and her allies were very confident that they had the numbers so getting only three votes should have triggered an interrogation. It would have been natural for Brad and Troyzan to go to Andrea and say that three people had promised to vote against her. I'm sure she also said that Sarah was with them so it would have put the cop in trouble.

As for Sierra, I do not believe she is that dumb. Everyone knows that all votes are read. Actually, seeing how production got Sarah to waste her secret advantage, I'm starting to believe that they gave her the F6 immunity as compensation. They could have had it all planned in advance.

You ask why production orchestrated that mess at TC. The answer is so easy to find that I'm surprised it didn't come to you: RATINGS! After Brad won immunity, they probably realized they were heading for a boring TC with almost everyone wanting Michaela out of the game. So, with that outcome in mind, they asked the players to spice it up a bit. The outcome is still the same but now they could present it as a game changing moment. By having total control of what they present, Survivor has a much easier time fooling its audience than a magician doing a live show.