From a meditator's perspective, developing a thick skin is the wrong direction for practice. That kind of thing creates a kind of contraction. The social mask constrains the natural expression of the person to the point where the social mask becomes confused with the person's identity. That's the stuff of therapy and existential angst.
What this guy is experiencing is not so much different from a meditator who has recently reawakened empathy, or a psychonaut whose psychedelic experiences open up to the world of emotions. "Coping" is no longer authentic, and is seen for the illusion that it is. For such people, the dysfunction is not in the awareness, but in that most people around you lack sufficient awareness -- yet think they are "normal".
Having some measure of "thick skin" is part and parcel for existence as a social animal.