The 2x factor reason is pretty intuitive if you understand that video compression is still fundamentally representing superpositioned signals from 2D Fourier Analysis and that multiplying by 2x the number of pixels in each direction is no different for perception than if we doubled the DPI. Double the DPI yields up to 2x the possible frequencies needing to be represented up to the Nyquist frequency that would cover each possible interpolated pixel. This is part of why noise in film or audio makes representation much tougher - noise is typically higher frequency and rather random (although distribution depends upon brown, white, pink, etc. noise).