The system OS has to have access to the game's front buffer to composite it with the system UI elements. Oh, I suppose conceptually the game content could be going to the composition chip and the system just sends instructions to that chip to scale and position the game content, without accessing the game's video buffer. So you'd have two buffers, OS and game, and the only place they meet is during composition for final output.
As for DRM, even if in principle they exist, no-one enforces them. You can screen capture on every device under the sun, from PC to tablets to PS4. I can't believe any dev releasing a game would then want to stifle viral marketing by not allowing people to share screens! Especially when they can share videos. The only reason for that is to inhibit pixel counters, and they don't necessarily need screenshots for that (DF captures HDMI out).