This is basically just a misunderstanding. There are multiple overlapping effects. Most of the 'hard' numbers for claims along those lines come from the flicker fusion frequency [0] around 50 Hz or so, which means that a video recorded at 25 fps and replayed by flashing every frame twice (like in old movie theaters) will not appear to flicker.
However, there's another important factor, which is that if you move an edge accross your visual field and sample at a certain frequency, depending on the speed of the edge, you might get a stroboscope-like effect and see multiple parallel edges. This is something a lot of people notice in 60 Hz computer rendered video, or when moving quickly under a lamp flickering at the mains frequency, because every frame is sharp without any motion blur. By contrast, you can run video filmed at an exposure time similar to the frame time at lower frame rates and it'll look fine, because the motion blur removes that stroboscope-like appearance.