There must be a connection to how doctors advice to talk to (even unconscious) patients who survived a stroke: the brain of the patient is still actively receiving information and constantly rewires itself while trying to process the data over and over again. In case with a complex programming problem, the person itself is responsible for the 'feedback loop'. Like how you can't stop thinking about the problem under different angles. Thus no need for external stimulus. I'm guessing the best time for that kind of processing is when one is asleep because there is simply not much else for brain to do in that state. Plus, when asleep, some long-term memory mechanisms kick in which make the already processed data more accessible and easier to work with. If there are some studies explaining the why's, I bet the medical ones focusing on brain damage and long-term memory would be the most related.