LAST EDITED ON 03-16-16 AT 11:07 PM (EST)Nah, Anna was more in a bad position. I think it's easy to look at the situation from the meta view and figure out the one possible scenario with perfect information that could've gotten her out of that situation. But that's ultimately fan fiction. I think you're very strongly overestimating Anna's value from the point of view of the rest of them.
I have a strong suspicion that Aubry and Joe are going to regret this vote. That being said, being able to see that problem in advance is a hard narrative for Anna to spin. If they boot Peter, they basically risk letting the 3 Beauties re-form again. That tribe had never gone to Tribal Council, there isn't any evidence they've really splintered in a significant way. They would just have Tai's word for it. Letting Julia link up with Anna next week basically means the next vote is controlled by Scot and Tai, two wildcards they don't actually know anything about yet. Or, if the plan is to get Scot out next and use the Beauties, they're basically risking their entire game on Tai/Julia/Anna not being a thing. If they are, they have no leverage in the next vote. Without perfect information, the next vote is a gamble either way for them.
If Anna's going to convince Aubry and Joe, it is all about constructing a narrative. And the narrative that taking out one of their own, who is maybe with them, in order to let the 3 Beauties arrive... Is a tougher one to sell than locking down Scot and Peter, who have already made it clear how dangerous the Beauties are. Anna is the "easy" play, and that's always going to be attractive to people playing from the top. I personally think they made a mistake, but I can see how they would fall into that knowledge trap.
If the alliance were Aubry/Peter and you would be pitching this idea to Peter (or if Debbie were there), I think it's more doable. It's just a much much much harder sell to players like Aubry and Joe.
Trying to pitch a counter-alliance against the Aubry/Joe would also be hard because if they could do it this week with Anna, there's very little stopping them from doing it next week with Julia. Anna is an extra number no one really needs. Especially for Peter who is trying to maneuver himself into the middle of an alliance.
No, throwing Tai under the bus is the "Taking the Obvious Answer" label, not the "Playing too Hard" label. Any brain-dead contestant would be able to see a simple 3/2/1 split and see where the votes might go to. Running to the 3 is the obvious answer that takes no absolutely no thought.