sudo cp -v /home/<your_user>/.dropbox-dist/icons/hicolor/16x16/status/* status/22/
sudo mv icon-theme.cache icon-theme.cache.old
You may want reboot to get it working (although it worked for me after a while).
That worked on system tray panel of 12.04 LTS Precise Pangolin 64bit. I've installed Dropbox from command-line
This solution is based on http://forums.dropbox.com/topic.php?id=35693