The basic question is: Does any other OS integrate the web browser into the OS? Microsoft have taken the position that the web browser is somply one aspect of the GUI, which is itslef fully integrated into the OS.
But here we are arguing over which particular part of a Linux distribution deserves to be called the GUI. "The GUI" is so modular and distinct from the OS that we can't even agree on what gets to be called the GUI! On top of the kernel there is (at least) the desktop manager, the window manager, the font renderer (probably) and the ... well I can't think what to call X, because there are desktops that don't even require X.
So there is a module that handles the pointy-clicky-mousish stuff; a module that handles the window widgets; a module that handles font rendering; a module that handles drawing things to the screen; and desktop managers like Gnome, KDE, fvwm and others which may or may not include any combinatin of the above modules, or may provide them itself -- at the user's option.
So instead of agruing about "what is The GUI" on a Linux box, can we just agree that it's pretty clear "The Gui" is not part of "the OS"?