One possible case example: Inspired by JA's comment on Policies can be changed.

How does an organization uncover those hidden issues that are really holding it back? A widget manufacturer had been doing some process improvements and ran into a roadblock when one manufacturing line was not able to keep up with the desired production rates. They had done all the things they believed would increase productivity of the line: tweaking the parameters to match the best ever production weeks; rearranging work schedules to allow for better flow through the system; offloading work that was more effectively done by other people. But none of these changes created a significant increase in production.

The team had to sit down and refocus on what they were trying to accomplish and to understand the basics of the process under which it was operating. After doing and redoing the calculations, it started to become clear what was limiting the production of the line: they weren't introducing enough work into the front of the line. Since not enough work was coming into the line, they could never get enough coming out the other end.

What was preventing the team from seeing this? There were policies in place to prevent waste. Starting extra work meant that there might be unused intermediate work to be thrown out due to the time-sensitive nature of the materials. Once the policies were surfaced, they could be attacked and either adjusted and removed.

Reference to "connected productivity"
Web Worker Daily had an article a few weeks ago on Connected Mode: Multitasking for Productivity. I don't like the idea of promoting multitasking, but the sense in which this article uses it is potentially interesting. We get work done through our connections, rather than as solo contributors. This sounds a lot like what I think of as connected intelligence.