It would have to get a lot nicer. I work in film and shooting an image of a TV or computer monitor is often a pain, even with high-end cameras, due to interference between the frame rates of the camera and display devices, as well as light intensity. For high quality results the typical workaround is to just throw up a grid pattern on the screen in question and composite in the desired image afterwards.
Is it possible to get results this way, yes of course. Are the results any good, not really. Commercial pirates work with people in the exhibition sector, amateurs rely on known weaknesses in popular disc formats. You'd have to be pretty desperate to rely on streamed media as your 'original.'