I don't think that there's any doubt that a departure in fog (< 1000m vis) is not VFR. The more interesting point is what operation benefit being IFR would confer.
The value of departing IFR in class G in good VMC is very limited: ATC provide separation from other participating IFR traffic, though most of the traffic about is likely to be VFR or non-participating.
Departing IFR with 8/8 ST/SC base 500ft tops 5000ft in a vis of 3000 m has rather more value. You probably won't see the traffic that you're likely to hit, thus having ATC separate you from other arrivals and departures while you're within, say, 15 miles of the field is worth having.
But departing IFR in shallow fog? The only thing you're likely to hit that you don't have the opportunity of seeing for yourself is someone attempting to use the runway at the same time. But separation in using the runway is part of the good ol' vanilla aerodrome control service provided to VFR flights too. Being IFR rather than VFR is, from an operational point of view, pretty much valueless.
That's what I understood as the point of Timothy's initial question, though I think some misunderstanding has cropped up as to whether it's legal to depart VFR in fog (by which I mean a vis forward from the cockpit of < 1000m). It's definitely not legal. It's just that it doesn't appear to do any harm to anyone except NATS shareholders...