Their should be a signal intensity level high enough to be distinguishable from nothing but still low enough to cause slight annoyance rather than traumatic agony over a short period.
One of the people in the story claims the florescent bulbs at the Dollar Store triggered her condition. If that's the case, it should be REALLY easy to verify some of these claims in a laboratory setting.
Heachaches caused by fluorescent lights are an entirely separate issue, considering they produce flickery light at odd color temperatures with weird peaks across the spectrum. Never mind that lots of establishments have things way too bright, and probably failing sockets causing extra fluctuations as well. I don't think it's disputed that anyone can see visible light.
I'll add to your comment that light sensitivity in general is a known issue with many people (eg autistics). They actually feel pain from seeing lights that are too bright including lots of sunlight or artificial light. So, one or more of these people might have this condition.
Well, programmers historically have tended to stereotypically prefer a dimmer milieu. Not to mention there are a number of simple physical injuries that can cause photophobia: <URL: https://en.wikipedia.org/wiki/Photophobia#Causes >
Overillumination has been known for some time to cause various other deleterious health effects anyway, and flicker aside fluorescents just put out plain terrible light. It completely baffles me why so many establishments install it (well, workplaces; retailers like it because it makes you buy more apparently).