A closer look at my server logs showed me that my problem was probably bingbot and BingPreview from a wide variety of IP addresses. I then found the following post on Google Groups which reported identical symptoms to what I was seeing:
"When I investigated an increase in direct traffic on some of the sites I run I saw that it was largely due to a big increase in "Mozilla Compatible Agent" browsers. Digging deeper into the data I see that of the roughly 29,708 "Mozilla Compatible Agent" direct visits to one of the sites from mid December to early February...
29,623 had Microsoft Corp as their network provider
29,623 were Windows 7
29,624 had a screen resolution of 1024x768
28,659 had Flash version 11.4 r402
29,670 were coming from the US or "(not set)"
12,952 came from Hialeah, FL
Hence it would appear a bot is not being properly excluded from Google Analytics reports."