the question is about the legality of the approach when common sense points out the shortcomings of the rules. We are not really discussing loss of visual in a shallow fog type of situation.
strictly due to law you may continue when you have a solid visual contact with the rwy or the app lights to decision altitude, and then finally decide regardless what the weather report says.
but i think its a theoretical situation that just the transmissometer is completely fogged with anything else good for a safe landing, never saw that in real life.