Arima - Rendering is the creation of an image from either another image or a model :http://en.wikipedia.org/wiki/Rendering_(computer_graphics) and blitting is the combination of multiple images into one (most often used to take all of the images in a scene and move them to the single image that is shown on the screen) : en.wikipedia.org/wiki/Bit_blit
It seems that the people that you know are confusing a Graphics Card with a Graphics Driver. The graphics card itself simply handles all of the processing that is given to it during the rendering stage, which then gives that information back to the main process, where the graphics drivers blit them to the screen. Graphics Cards are optimized to the fullest extent possible, but they do not clip any screens that are given to them, as it is not their task to do so (since that would make it necessary to have a graphics card within your computer). When they pass the images that need blitted to the Graphics Drivers, they are then cut down to fit the viewing screen.
This means that the Graphics Card is still doing all of the calculations that it might need, unless you pre-trim your viewing screen.
Check out 3D Game Engine Design by David H. Eberly (http://bit.ly/Z0quBr), or Berkeley has a free online class that touches on the topic (https://www.edx.org/courses/BerkeleyX/CS184.1x/2013_Spring/about).