I'm not quite convinced of the article's thesis. It may be true that the brain doesn't chug along on a background problem continuously for days, but instead it checks in on the problem every so often when it is in a different state. But the act of reconsidering a problem from a different mental context is the essence of problem solving.

The experiment involving retrieval of foods and countries is suggestive, but I think it cannot be generalized outside of that experimental paradigm. The same for doing arithmetic in one's head. Creative problem solving is a different beast, and the flashes of inspiration described in the article which take place after a matter of hours or days are indicative that the mind revisits the problem in the unconscious.