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Eliezer's post Conjunction Controversy (Or, How They Nail It Down) also covers some of the research showing that the conjunction fallacy is not just due to misunderstandings.
It could be in part due to training.
Reyna & Brainerd's Fuzzy-trace Theory research suggested that the conjunction fallacy gets more common with age.
And given that some of my guess-the-teacher's-password heuristics more or less directly invoke conjunction fallacy (Given A, B, C, and D, where D is A+B, D is more likely correct than either A or B), I'm inclined to suspect that education might be strongly reinforcing the bias.