I definitely agree that the brightness of the screen matters. And further that the brightness of the surrounding area matter. That's why I use
f.lux in Windows to control the brightness of my LCDs. I am at my computer from the moment I wake until the moment I go to bed on an average day, minus any time I spend reading. I definitely find that if I am in a dark room trying to read on a bright white screen, it hurts my eyes. This is why I read grey on black on the iPhone, with the brightness turned way down.
My theory on the matter is that your eyes get tired of adjusting the aperture from when you switch back and forth between bright and dimly lit areas. This leads to a kind of muscle fatigue. Having your screens match the brightness of your room decreases the brightness contrast so your pupil doesn't have to dilate and shrink with as much frequency.