The Walrus and the Carpenter led the poor little clams astray. I feel you may be heading down a similar path my friend. Alex, making the assumption that is the young girl’s identity, would have lived with the Others her whole life. The most inept cult leader could brainwash a child given those conditions. I tend to believe that if Alex thinks they were going to kill her, they were indeed going to kill her.

On the other hand, what if they instructed Alex to aid in the escape.

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"Malinois... It's kinda like a bullet. Only it has four legs, teeth, goes around corners, jumps over obsticles, and never misses."

- The DogFather