Interesting theory Scott....however, let me express my idea about the issue.
I don't think the refresh rate of the screen has something to do with response time. Maybe if the native content is not matching your refresh rate, the worst thing you will have is pulldown judder (24 frames on 60Hz monitor, or 30 frames on 50Hz monitor etc). If we presume that we receive 60 fps (as a native content) then either 59,997 or 60 Hz will work just fine.
The issue with ''clicking'' has to do with 2 factors.
The output lag of your screen and the response time of your mouse.
The best monitors for gaming (undoubtly) were CRTs. The had 0 lag...0. Right now LCDs have good lag timings but that depends on the panel and the dimension. As you go big, the output lag increases. The so called gaming monitors with 5-10 ms lag, is a very good option at 24-27 inches and will cover most of player's needs.
Let's go to the mouse now. Same story. Gaming mouses (wired naturally) are faster and most responsive while you play your game.
There's a third factor which i prefered to leave it out....the hardware of the system and the OS, but these are deep waters, so let's stick for now to the above two ''prime suspects'', mouse and monitor.