EMLab P&K also tested refrigerator door handles and produce. It found similarly unpleasant results. Take a look at a complete breakdown of those findings here.
While the results aren't thrilling, the study is limited. It looked at just two stores in each category. Inside each store, it swabbed five carts, three pieces of produce, and three fridge door handles. So, there are definitely germs, but the sample size is low enough that it's dubious to extrapolate the results nationwide.