I can think of 2 hypotheticals.
1. You arrive VFR, no qualified weather observer, the fog is just covering the weather machine but not the runway.
2. The AWOS drops below mins after you cross the final approach fix.
In either case, like the OP says, it's flight visibility vs. reported visibility.
The first, you have to make the case you had 3 miles (or 1 mile daytime in G), all the way down to landing. Not necessarily dangerous, but someone might raise their eyebrows with legal concerns.
The second, you're still legal to take a look, but if you land, you have to make the case that what you saw was at or above minimum flight visibility (ie "I could see ____ from the threshold, from which I determined I had ____ feet of flight visibility").