Sorry as this diverges offtopic but it was a research project of mine so hence the interest.
You are right that the limit of discrimination that I quoted was for active touch along a linear surface not along a curved plane. The edge sensitivity of mechanoreceptors do change with the curvature of a plane and hence if the finger is static then it cannot provide information about a curved shape but again this situation changes when the finger is moved along a surface. The signals from the afferent mechanoreceptors in the fingertips and receptors in the hand,wrist, and arms (depending on the radius of curvature)all gets processed in the somatosensory cortex to give the final impression. The fingertip does still give touch discrimination or else you could not tell the difference between a smooth curve or a smooth curve with "bumps" as you run your finger along the edge while simultaneously moving your hands, wrist, arms, and shoulder to follow the curve.
There is no methodology (at least consistent and reproducible) to measure exact tactile discrimination without introducing some bias therefore vibration, which is easily measured and reproduced, has been used as an adjunct test to determine the severity of peripheral nerve dysfunction and to my understanding why ISO 13091 was established...to standardize testing techniques/equipment to validate the thresholds in healthy subjects and possible peripheral nerve loss in patients only in regards to vibratory sense.
I share your concern in regards to the comment "Also, if you run your fingers around each watch, you can feel the difference in Lange's better finish" It leads to many assumptions which may not be justified or accurate. My comment was directed more towards the idea that you need to give our fingers and brain more credit than only a discrimination limit of 0.8mm