Theres nothing wrong with 60hz if the flicker doesn't bother you. I'm not an expert on it, but refresh rate on CRT's does not impact your performance. Your brain interpolates frames (well actually, your retina splits up frames into 7 distinct "information distinct" frames anyways, and vector motion is only 1 component, but I digress) anyways, so unless redraw rate is severely low, you should not have much problem. I'm not sure how refresh rate affects LCD's, but I suspect it works differently, since the speed with which the liquid crystals can change state is the limiting factor for motion response there.
I suspect the talk is mostly related to input/output lag, but that has little to do with refresh rate (except, possibly for timing issues such as cadence issues with 24fps material and 60hz LCD's). It is a processing issue in the LCD (overdrive being the prime culprit), and that would certainly effect reaction times in fast paced games, and would be especially pronounced in low-lag matches online where your opponent had lower output lag.
But otherwise, 60hz is more than fine. You can have faster reaction times than 1/60 s with 60hz monitors because of your ability to predict motion vector. If your game is running at ~120-200 fps (depending on the person) you are maxing out the reaction times of most people even with a 60hz CRT. Peace.