Specifically every link they every clicked on, on every web site.

Yes some fraction of this was on google. That's not cheating. No content from google was transmitted back to Bing. Just the next site the users went to. Is Bing supposed to go through the logs looking for visits to google and then delete the rest of the session because it might indirectly reveal something about what existed on the google page?

I should own my records about what pages I go to, not Google. If I share them with Bing it's nobody else's business.