I think that's a misleading stereotype. It all depends on personality, temperament, upbringing, religious beliefs... all kinds of factors. Age isn't necessarily one (although it can be, I suppose). Some people are just sensitive or sensitive to particular things. My eldest son (20), who certainly wasn't mollycoddled with what he watched growing up, couldn't sleep after watching Alien and Psycho. Both completely freaked him out. These films are classics, yes, but I was surprised they got to him as much as they did.
Classic literature is awash with some of the most graphic and horrific violence you can possibly imagine. So is Greek mythology, the Bible, etc, etc. I think the human race has always defined itself through storytelling, some of it exceptionally nasty. This is nothing new. But some people simply don't like gory or violent stories.