Since those X11 extensions are hacks onto X11 to enable such exposure, I'd say the GP is right. X11 doesn't expose that kind of stuff.
They're not hacked on, you're just misunderstanding what the word "extension" means in X11 terminology. X11 extensions are named groups of commands that an X server can optionally implement. The core X protocol includes commands for checking what extensions are available, so that applications can use those additional commands when they're supported, or work around the lack of them (or just display an error message) if not.
This is a designed-in extensibility mechanism, not some afterthought kluge. Many "standard" facilities are provided through X11 extensions, such as displaying anti-aliased text (with the RENDER extension, though it can also be done in a slower way if RENDER isn't available), overlay-based video playback (with the XVideo extension), changing screen resolutions (RANDR), turning off the monitor to save power when idle (DPMS), and OpenGL (GLX).
OpenGL, by the way, has a similar extension mechanism, and that's what allowed it to support new GPU features (such as multitexturing and pixel shaders) as they were developed, without requiring a whole new version of the core OpenGL spec.
Desktop compositing in X11 is done by asking the X server to give each window an offscreen area of video memory to draw itself into, rather than drawing directly on the screen, and then asking the OpenGL implementation to make these offscreen areas accessible as OpenGL textures. The compositing manager paints the windows onto the screen by putting these textures on rectangles, applying whatever visual effects it wants to display (like the Compiz cube), using normal OpenGL drawing operations. The command to make the X server redirect window drawing to offscreen pixmaps is provided by the COMPOSITE extension, and exposing those pixmaps as OpenGL textures is done with a GLX command, GLX_EXT_texture_from_pixmap.
I've used Compiz and Beryl, they both crash regularly and slow my laptop significantly (a couple years old, but runs Vista just fine). Gnome-Shell looks ok, but it isn't exactly out yet (you can get a preview from live.gnome.org) so it's hard to compare it.
If Compiz is unstable, that's an application bug that doesn't really have anything to do with the design of X11. The compositor in Metacity (the GNOME window manager) is pretty stable (I've been using it for several years), and its scenegraph-based successor (called Mutter) is the foundation for Gnome-Shell.