I think this is just uninformed and outdated scaremongering. I would think that if there is an effect it is very uncommon and if there is any link to LCDs it is probably difficult to substantiate, which is why you don't see any real scientific articles on the subject.
A quick look over the wikipedia article for fluorescent light shows this:
LCD backlights are usually cold cathode fluorescent lamps which operate very differently from your standard overhead lamps at much higher frequencies and do not "flicker". He doesn't directly mention CCFLs in his article, but in passing he dismisses his own concerns as fixed by "newer technology". He's even using LCDs himself: