I like the rec.puzzles answer

... In this case, the hidden assumption is that P(predict X | do X) is near unity, given that P(do X | predict X) is near unity. If this is so, then the one-box strategy is best; if not, then the two-box strategy is best.

I think knowing who is doing the predicting, or how the predicting is done affects the important probability; how likely is it that my choice affects the prediction. I'd have to agree, knowing who the predictor is matters.