I'm not the GP, but it makes sense to me. I can't even see a difference between 24 and 60 FPS. It has to get down into the teens before I can tell. I haven't capped my graphics like that, but that's more because it never occurred to me than because it would bother me.
Honest question, not intended to be disparaging: do you not see a difference between the various animations on [1], for example? To me, they are very apparent.
This website does things a poor justice and doesn't seem very accurate. For example, I tried this on my linux work computer (which doesn't offer vsync, or a graphics card) and compared it to my gaming pc. The non-vsync version looked much better than the vsynced version.
I went outside and took a 4k video at 24fps and played it back. It looks smooth as butter, just like a movie. Then I took the same video, but recorded at 60fps and re-encoded it in 24fps. It looks like the example on this website, where it looks jumpy.
The bottom one looks different. Like I said, I can tell once the FPS gets into the teens. The top two look exactly the same to me. I realize they are different, but I can't see it.
This is better, because we're talking about the lower range right now anyway.
That said, I think the difference between 144Hz and 72Hz is a lot more subtle and can't be seen if you try to glance at them directly. Try viewing them with peripheral vision and there's a difference in smoothness. That shows up in things like moving a window around (or even just moving a mouse). It makes a huge difference in input latency/response, but the difference can't be seen easily by just staring directly at a moving image.
Wow! I can easily see the difference between 120 Hz and 60 Hz. 30 Hz (bottom one) looks absolutely horrible to me. I guess there is a large gap between how various people perceive the world.