This is interesting. If LED lights pulse so quickly that we don't notice the flashing, how are these people able to perceive it in a way that causes them pain?
1) I think it is totally possible that small scale effects can bug you at different layers of your neural processing: just because it is extremely difficult for me to perceive a sound doesn't mean my ears aren't being affected by it and even providing a signal to my brain with the information where it is being discarded actively.
2) They often don't? A lot of LEDs flicker at something like 60Hz. Sure: if you stare at the light you might not notice it blinking, due to the limitations of the sensors in your eyes that can weirdly "get tired" of looking at the same thing for too long, but if you move your eyes across the light quickly you will see it blinking as now you are getting a broken dotted line carved into your vision. I find this maddening when there are such lights in my peripheral vision.
Different parts of your eye are attuned to different frequency responses. For me, it is easier to see flicker in my peripheral vision rather than my direct vision, so if something is off to the side it can be more annoying than something right in front of me.
That said, I can eliminate all annoying flicker by making sure that all of the things that flicker aren't mixing down into ranges that start to annoy me. For example if you have some LEDs that are running at 15Khz and some that are running at 15.1Khz they can set up a beat frequency at 100Hz that is annoying. I had some dimmable can lights that did this and figured out that the PWM was local oscillator based (R/C if you can believe it) rather than crystal based. I found lights that used the line frequency to drive their oscillator so they are essentially all in sync (at 2.4KHz or so, so not noticeable to my eyes)
Back when DLP projection TV's were popular, I used to see the "rainbow effect" and it was distracting enough that it was hard to watch anything on the TV.
Many people can see it, but don't really notice it... until you point it out. I pointed it out to one guy that owned his TV for a year and never noticed it, but after I pointed it out to him, he couldn't stop seeing it and could never enjoy his TV after that.
From my personal anecdata, they don't perceive the LED flashing directly. Objects in motion look weird under some LED lighting. Motion doesn't look smooth. It's like a weaker version of looking at moving objects under continuous camera flashes. The effect isn't super explicit, but moving objects become jerky. Try looking at a fan under the lighting of cheap Christmas LEDs.
More sensitive people will notice this effect even at a few kHz when an object lit by the source moves quickly or the viewer's vision pans across the light source. Even faster PWM up to a few kHz is visible to some people this way.
Everyone can see the flashing. You can become aware with a bit of effort.
Find a LED light that isn't on a continuous DC power supply. Christmas lights work well for this.
Pick two objects, one far to the left of the light, one far to the right. Focus on one side, while making sure the other object and the light remain in your field of view. Next, glance at the second object so your eyes quickly travel across the LED.
If you have christmas lights you can exaggerate the effect by spinning the cable. You don't need to move your eyes at all in that case.
If you have manual control over the shutter speed on a smartphone or other electronic rolling shutter camera, just turn the shutter speed high. It's possible to detect flicker up to at least a few kHz this way.
The pain just comes regardless of whether or not you actually perceive why. For me it's kind of a cramping sensation at the back of my eyes and if there is no other light source (think christmas tree with cheap LED lights in an otherwise dark room) i will also get nauseous.
If you're shifting your view/moving your head you can easily perceive the flashes.
You can't see UV light, but if bright UV light shines into your eyes it can make you blind. You don't need to be able to consciously perceive something for it to have a physiological effect on you.
I noticed that with some tvs if I look at something else I can see them flickering in the side of my vision but if I look directly at them they look fine.