Just because you've never had a problem doesn't make it non existent. No one is going to take away your new shiny monitor.
Most companies run infrastructure to failure. That means fluorescent lights with magnetic ballast that flicker at 60 Hz x 2. Previously, an old CRT with worn out phosphors running at a close frequency would have very noticeable flicker. The beat frequency (difference or lack of sync between two rapidly flickering sources) is what matters. Personally I could see some flicker with a monitor under fluorescent lights up to 70 Hz. Some coworkers always left their CRTs at 60 (where flickering was most noticeable) and we're never bothered. LCDs with CFL backlights generally don't have Mich of an issue (high frequency driver due to size).
I can see how an LED backlight with faulty circuitry could become an issue, especially if it has a flicker close to powerlines frequency. Again it would not be noticeable to everyone. That doesn't make it psychosomatic. Just means the guy who sees it has a slightly different visual cortex in hos brain from you (faster clock speed)? Stop throwing around this nonsense and accusing the OP of being allergic to WiFi too.
By the way, if you ever work in a large company or government, you often will be stuck with degrading equipment for quite some time. Especially outside of IT.... I feel sorry for the OP if this is the case as if his boss can't see it, he's stuck with it until it breaks or he quits.
Also someone mentioned LED lights on cats. Cars run off of DC, but voltage regulators and alternator can add a pulsation to any lighting.