This is kinda true. In my opinion there is no point in locking the fps to 60 when you could also be getting 90 fps on a 120hz screen. Might as well use those frames as long as they come in regular intervals.
The lower the fps / hz the bigger the intervals between frames and refreshes and the more noticeable the stuttering and lag. If you exceed consistent 60 fps it should all feel roughly the same. There is no need to get an expensive 240hz screen to game at 100 - 120fps. 120hz or 144hz is enough for that. (As always depending on what you do with it, a professional CS player might need the higher Hertz)