According to Feeling Small: Exploring the Tactile Perception Limits, studying randomly selected people with no previous experience:
> the lowest amplitude of the wrinkles so distinguished was approximately 10 nm, demonstrating that human tactile discrimination extends to the nanoscale.
Leister stated in the interview Making the world's perfect Kilo :
> this can only be done by hand because you actually have to feel what is happening. When you’re taking off a nanometre or 5 nanometres, or 10 nanometres or 20 nanometres, some of the errors we’re trying to correct are in the vicinity of only a few nanometres.
So human touch can work down to the 10 nanometer scale with no specific training, and Leister isn't really claiming to be much better than that.