Give their docking simulator[1] a go on a phone or tablet - I was dubious at first, but even on an iPhone I managed to complete manual docking on the first attempt. It turns out flying a spaceship is very different to flying a plane, and rapid inputs just aren't massively important. Generally your edit is probably true as well - in standard flight everything is meant to be on autopilot using predefined routines for the mission, computers are just significantly better at performing a 16 second burn at 82% thrust at precisely T+12:48:16.