Sounds like to me that maybe its not about how thick their skins are but about not taking the job personally. If you view a job just performing a function for money and just focus solely on the job it would look the same. Ignore other peoples drama, personalities, work ethics etc. Just do the job and focus on that ignore the drama, the gossip, and focus on doing your job well.

I manage staff and my best employees would seem stoic but really they just had focus, good work ethics, and a kind of get in and get out mentality. No gossip, no hanging out with their coworkers. Work was work then go home.