404 Titan
The problem is that the horizontal visibility was 300 metres at ground level up to 2 metres and 800 metres visibility is required from the Cat 1 DA of 357 ft with an actual QNH all the way down to the runway.
Utter the word "mayday" and that requirement goes out the window.
At the point that the wheels would have touched the runway, the pilot's eyes would have been well above 2m, so you point is pedantic at best - he would never have entered the shallow fog, only his undercarriage would have. The only consideration is slant vis, but with what was obviously radiation fog that was rapidly burning off, and a reported vis of 300m, there is no doubt at all that runway markings and lights would have been visible through the layer.
I have also had extensive experience of fog (in the UK, the home of fog), and the shallow stuff is generally not a problem. It's the stuff that forms in a layer 200-300 feet thick that will get you.