Some people ARE sensitive to reflected LED light in any quantities. I'm not one of them, but direct LED light is bad even in my peripheral vision. Also, LED bias lighting (which is to say not the primary lighting, but for accent purposes) also seems ok - I don't have headaches when I walk under a bridge with LED lights underneath, for example. I have some LED bulbs in the house, and while I don't like the way they light up a room, the soft/yellow ones are ok as long as I don't ever have to look directly at them, so for example they work fine in the hood over my stove, because the light is both behind a metal lip and under a translucent plastic cover. BUT LED-lit refrigerators piss me off, especially the kind where the LED's are more forward-facing as they are in many new beverage fridges at the grocery, for example.
It's really complex. LED's - whether from imperceptible flicker or from brightness or from spectrum - are an issue. But not the only issue, and almost impossible to separate from other issues as a source problem.