Interesting topic. Three things that came to mind while reading through the posts:
1. Many moons ago, Roberts sr had trouble going fast enough around Suzuka. Instead of continue circulating, he went back to the hotel and had a think. A few hours later he returned to the track and said he had found 2 seconds. Hei proved it by going 2 seconds faster.
2. Darren Binder, Moto3, says he has no braking points, he brakes when those around him does. He's fast, but cause a lot of havoc and crash frequently.
3. Rossi, and others, often try a fully new and untested setup before races when they haven't found a competitive setup during practice. At least in the case of Rossi, it seems to pay off more often than not.