I think the idea is that you have do something with the full intention of "wasting" time to trick your mind into thinking creatively. I usually don't step into the shower ready to tackle a hard problem -- it's not the best place to do any kind of work. And I'm sure if I decided to solve a particular problem in the shower, I would probably not come up with a solution -- it's when you don't intend to work, do creative solutions appear in front of you.

When you decide to solve a problem, your mind goes at it with a very direct engineered approach which may not reveal solutions that come from a different angle.

Also, I've found when I can't think of solutions, it's usually due to my mind being tired, and the best way to solve it is to actually waste time -- go for a bike ride or something that forces your mind to stop thinking.

Personally, it took me a long time to realize that time was not wasted. Mostly because it doesn't feel directly productive.

Also, having your mind actively on and turning over a problem defeats the purpose of letting your mind wander freely in search of serendipitous solutions. Having it actively "on" is the same as keeping busy.