OK, A small clarification: the 3D skybox is not always fully drawn to the display buffer: when the game comes to render it, the only pixels of the 3D skybox (and 2D skybox behind it) that are actually drawn are those where the z-buffer is empty, i.e. where something in the world has not already been drawn. But that is the final stage of rendering; all the polygons, textures, entities in the 3D skybox will have been included in all the lighting and transform calculations up to that point. (It is also possible that the game will not render the 3D skybox if none of the visleaves in the PVS use the toolsskybox texture, but I don't know whether such an optimisation is used.)
What's happening in your two pictures, Misteri, is this: The game draws the world, with both z-buffering and z-culling so that things further away correctly get obscured by things closer to hand. It then draws the world's wireframe, without z-culling, so that the wireframe is visible above all the world objects. It then draws the skybox with z-culling, at a z of 'infinity' (so it never appears in front of any of the world); and finally draws the skybox wireframe, still with z-culling. The 3d skybox is still included in rendering calculations, but it and its wireframe will always appear to be covered up by any world objects..