This is one of those really frustrating finds, which if only the title mentioned the right words, would have been done in minutes.
Setting up a group policy for use with some on-screen tests that we wanted to perform. We wanted a custom desktop with only the icons that they required.
Little did I know after 15 minutes searching through a list of GP settings that the option to disable the All Users Desktop is called Remove Common Program Groups from Start Menu. How un-obvious is that? Not even the setting description mentions that it has an effect on the Desktop!
For everyone else out there looking for this setting:
User Configuration –> Administrative Templates –> Start Menu & Taskbar