I don't care how good the pilot's eyes were; there was zero visibility outside that airplane. That fog we were in was the metaphorical "pea soup", and he could not possibly have landed visually.
What you see from a passenger window has little relationship to what the pilot is looking for and can see out his windshield. The pilot is looking for lead-in lights (there's a lot of them) and a sequence flasher that creates the effect of a ball of light starting at the beginning of the lead-in lights and traveling to the runway. In low visibility the tower will typically turn them up to maximum intensity. These lights are very bright, so much so that after catching sight of them I usually asked for them to be turned down. None of this light system is visible from the passenger cabin of a large aircraft save for the fact that you might notice a glow outside as the airplane passes over them when it's dark.
the pilot came on the intercom and announced that it was too foggy down below to land, but we still had plenty of fuel reserves left and so he was going to fly in circles for a while and see if the rising sun didn't burn off some of the fog.
Another thing that the pilot can do if he has the fuel and if the sun is about to set, is to loiter until it gets darker. The RVRrunway visual range (RVR) will generally increase considerably in the dark.
There are other things at play as well. In patchy and/or blowing fog, what the RVR reads may not accurately reflect what the visibility is anyplace in the runway environment save where the RVR instrumentation is.
Occasionally, local politics can also be a factor. In the 1980s I used to fly into an airport that had as its only air service the commuter airline I was flying for. The local government and chamber of commerce very much wanted to keep that air service. The problem was fog. An unwritten accommodation was reached that took advantage of the rule that once inside the outer marker, you can continue the approach even though the RVR dropped below the minimum required. We knew that if the reported RVR was right at the minimun required when we were cleared for the approach, we might well be told after reporting passing the outer marker that it was a lesser value.
In two years of flying for that commuter, I never failed to land on the first approach at that airport and neither did most of the captains.
I suspect that in today's hypersensitive regulatory environment, this accommodation might not be possible, and I also don't know if the rule is still in force that permits you to continue an approach once inside the outer marker.