The human doesn't make a choice here. The alien does. Or rather, the human, by being a two-box human or a one-box human, directs the alien to put the million in or not. You make the choice long before you enter the room, through all the actions of your life that will make you the predictable being the puzzle stipulates that you are.

You think the alien can't exist? Actually, we could almost do this today. There are drugs, like Versed, which inhibit your ability to store long term memories. I could give you Versed, pose the problem to you, see what you do and then wait until it wears off. You will have no memory of the puzzle. (When this was done to me, I remember the injection, but nothing after that, even though I talked to people.)

Anyway, I give you the drug again. (If it weren't an injected drug you would have no way of knowing this is the 2nd time, for for this hypothetical imagine you think the injections are for something else.)

Anyway, now I can predict what you will do very accurately. Probably not as accurately as the alien, but so well that the result is very similar. Those who are the sort who pick one box become millionaires, those who aren't, don't.

Now imagine something better than Versed, something I can give you without telling you, something that doesn't sedate you or generate other visible effects, something like the Men-in-black pen that just erases a segment of memory if you will. It's not as science fiction as it sounds, the drug I describe is real and is used in medical procedures where they want you to be awake but not remember the horror.

Now do you understand the problem better? You understood it better the last time I explained it to you...