I think the theory theory is that if actions are extrinsically rewarded, the narrative that gets formed is "I did X because the teacher gave me candy", not "I did X because I really like and value doing it." Thus later, when there is no reward (or punishment) offered, the person doesn't have a narrative for why they would want to do X anyway.

Agreed, though–it confuses my intuition, that rewarding a behaviour would reduce intrinsic motivation.