If one remembers that the subconscious makes up approx 80% of the brain[0], there is a lot of problem solving potential in switching off the conscious and "backgrounding" problem solving to the subconscious.
Which in a way, the author is indirectly describing. Engaging in activities that are "automatic" (e.g. showering, long walks) also allows the conscious to drift and frees the subconscious to interrupt the conscious with some solutions. Hence the best ideas under the shower.
Taking a break from the problem can sometimes be the faster way to a solution, illogical for modern bosses who believe only working on the problem will solve it.
[0]=if you don't believe this then try to consciously pick up a cup of coffee and drink from it. The coordination of muscles, swallowing, and everything besides is the subconscious. The conscious, if at all, had the thought "I want to drink coffee" or it might just have been a feeling between messaging and eating a breakfast toast!