NT, 2k and XP will run fine without a browser, but
Windows won't. Windows is the user interface that makes it possible for apps to interact with users. Yes it sits on top of the OS, but the GUI DLLs cannot be removed without apps breaking.
The Internet browser sits on top of all this and can be replaced or disabled, but the underlying UI objects cannot be removed or replaced.
I believe that what Microsoft is saying is that the browser is a trivial app sitting on top of stuff that can't be removed.
True. The layer you're talking about is the user-interface layer between the OS and applications -- widgets such as menus and list-boxes. No, you wouldn't have Windows without the taskbar and mouse, or the radio button or check box.
Those are parts of the user interface. When you write an application program for Windows, you draw on these objects to display your application.