But even now, many video sites employ DRM, and only the weakest levels of DRM streams can be recorded off the screen. If they crank that up, which is perfectly possible today, the screen recordings only shows a blank rectangle, because the encryption goes from server to video card. At this stage, "hdmi recorders" are the next level - they capture the audio/video stream from the hdmi cable output for example.
Even further, there is technology to encrypt from server to screen. I'm not sure on the rollout on this one. I think we have a long time until this is implemented, and even then, I'm sure we will have the ability to buy screens that fake the encryption, and then let us record the signal. And, for mainstream media, there will be pirated copies until the end of time I think.