As to Googlebot's use of cookies - there is debate and folklore, but in the tests I have run I have not seen Googlebot ever send back a cookie that I have sent it.
Google do manual reviews of pages, and I am confident the site in this example (for the case in question, at least) would pass that without a problem.
I'm (genuinely) interested in your proposed solution for dealing with the duplicate content problem. The problem with the Panda algorithm is tends to be a bit touchy and it seems easy to fall foul of it even with innocent situations like this one.