OK...real-world example time here. A bunch of years ago I was flying a Jetstream and cleared for the ILS 16R at Seattle. Conditions were such that there was a fog bank right over the approach end of the runway--and the arrival end transmissometer.
The rules say that to be legal to start the approach we have to have landing minimums at the final approach fix--in this case a runway visual range of 1800 feet. IF the weather goes below minimums AFTER we cross the final approach fix, we can continue to decision height and IF we have the minimum visibility when we get there, we can land.
So, back to the Jetstream: We were cleared for the approach and halfway down the ILS, the airplane behind us was told the RVR was 1600, thus below landing minimums. The kicker was, the fog bank extended less than 1/4 of the way down the runway and I had the last 3/4 of the runway in sight for the entire approach. So, I landed. Had to go slightly above the glideslope to avoid going into the fog, but I was able to touch down safely. As a CYA move, I told the tower as we were turning off the runway that we had visual on the runway the entire way down the approach.
So, was this legal? Probably technically not, since the touchdown zone transmissometer was supposedly below minimums when I got there. Was it safe? Yes--the fog bank only extended 1500 or 2000 feet down the runway and I had 8000 or 8500 feet visible; I'd made hundreds of approaches to runways much shorter than that, so I knew I had adequate runway available.
BTW--in reference to the comment in the first post here about the Jetstream pilots. We hand flew everything. Six or eight approaches to minimums a day hand flown through the turbulence and ice and clouds were just another day at work. Unfortunately I'll never be the instrument pilot I was back then.
The "keep my tail out of trouble" disclaimer: Though I work in the airline industry, anything I post on here is my own speculation or opinion. Nothing I post is to be construed as "official" information from any air carrier or any other entity.