"Troy wanted Mike gone from Day 1, per both of them."But, at that time, Troy was insisting on eliminating a girl in order for Kim to prove her loyalty. Troy doesn't vote against Mike unless she plants that seed and he had the immunity idol to save Mike if he had seen that Kim was setting him up. It was brilliant and not just editing.
Kim was quite slow in the F5 IC; she was last off the rope net and then had trouble solving the combination lock. Tarzan could have beaten her. You can't say for sure he wouldn't. Besides, Kim couldn't know if the next challenge would have required upper body strength, something that favors a man, any man, Tarzan included. She had to boot him then. Great manipulation.
Every winner needed luck so that point is moot. Even Brian. Even Rob.