Brain-hand response isn't what it's about here: it's about synchronicity, the notion that clicking the mouse and effects on screen occurring at the same time. It's quite easy to see (and hear) relatively small differences between two events that are supposed to happen simultaneously.
For example, of my two monitors, one is lagged by one frame. I can see this easily by taking a white window against a black desktop, moving it so that it straddles both monitors, and moving it rapidly up and down: the monitor that's a frame slower makes the window look a bit like it's made of rubber, that it's bent away from the direction of motion. And that's just a 17ms difference in two events that are supposed to be simultaneous, an order of magnitude less than your factoid of 200ms.
For example, of my two monitors, one is lagged by one frame. I can see this easily by taking a white window against a black desktop, moving it so that it straddles both monitors, and moving it rapidly up and down: the monitor that's a frame slower makes the window look a bit like it's made of rubber, that it's bent away from the direction of motion. And that's just a 17ms difference in two events that are supposed to be simultaneous, an order of magnitude less than your factoid of 200ms.