Where have you heard that about Google? I've heard good things about their (current) culture, especially in regards to 20% time. Have I been misinformed?
I don't think you've been misinformed, I personally think the marketing of the 20% time idea is better than its actual implementation.
Pitching the 20% time ideas to management is kinda killing the concept. Managers aren't particularly inclined to incorporate hours into your schedule, especially if that time could be used boosting their metrics.
I also find that the definition of 20% time varies a lot between individuals. For me, it's "All that time when I have nothing better to do, when I get to work on whatever I want" - in some weeks, that can be 80%, in other weeks it's 0%. I have a friend who spends one morning a week working at Google Research, and that's his 20% project. I have another friend that taught Lego Mindstorms to 5th graders one day a week, and that was her 20% project. I have another coworker that started working on a new project (sponsored by a different VP), and that was his 20% time. I have a few coworkers that basically do whatever they want - actually, my job description is pretty much like this now - and so it's all 20% time.
Actually, for a lot of my coworkers, the reality is probably much like it is in many other large organizations with decent management: "As long as you get your work done and are aware of the organization's priorities, you can do whatever you want." I know someone who moved to Uganda without telling his manager and regularly works from Paris, Thailand, Budapest, Vienna, Prague, etc. - his manager doesn't care, because he's responsive to e-mail and gets his work done quickly.
Regarding the idea, I think it is brilliant. We all know that we are stuck on a problem, going away from it for a while is healthy and productive. I do think it works on a bigger scale.