They're somehow getting the stats via the browser, not Google Analytics. Get that and lots of things make sense.
Just to point out that there is no "Exit Rate" from the side Google sees the pages. Google Analytics data can't be used, because it can be manipulated. Analytis is an API, you can do whatever you want with it. For example, inflate or deflate Exit Rate.
Having said that, you can discover a correlation between Panda and or Penguin and your Analytics Exit Rate, but there is no point trying to figure it out how Google measures or uses Exit Rate. They are apples and oranges.
About the browser and other Google products, anybody knows how the provice policy allow / disallow getting signals for search? I have no idea.