One thing that sticks out is that these guys aren't team players. Speaking strictly of strategy, I think the best strategy for a participant on this show is to voice his opinion and if the team leader shoots him down, shut up and do his best to make the leader's "vision" work. If it does, great. If it doesn't, then you can blame the leader in the boardroom. How could Trump fire you in that situation? You didn't make the bad decision. You were a team player. And you worked hard to help your team win.
In fact, if you really wanted to be sneaky and thought the leader was weak, you could wait until he tossed out his idea, THEN you could pipe in with some contrary idea, knowing that it would probably be shot down.
Lizzy wasn't very effective, granted. But I thought her team stunk, undermining her at every step.
Too bad they didn't have a real coup and fired her. Trump would've been impressed with that.