The myth
Any frame beyond your monitor's refresh rate is completely wasted. We almost say this sentence on our own optimisation page, and yet it is too simple.
What is actually true
For your eyes it holds. Your monitor displays a fixed number of frames per second, and anything above that you simply do not see.
What you can notice is the time between moving your mouse and the picture on screen. NVIDIA says it themselves: in general, higher FPS correlates with lower system latency, even though the relationship is far from one to one. That latency is exactly what you feel as directness.
The grain of truth
This time it sits on the other side than usual: the myth is right about seeing and wrong about feeling.
What to do instead
If your monitor supports FreeSync or G-Sync, turn it on: the monitor then matches its refresh rate to the card's frame rate, and AMD describes the result as tear-free, flicker-free gaming. How to set it up, and why capping slightly below the refresh rate pays off, is covered on the optimisation page.
Without variable refresh rate, and in competitive games, you can happily let the card render past the refresh rate: you keep the lower latency even though you never see the extra frames.