Do you allow your children under 10 years old to watch horror movies?

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I posted this discussion because, on my way home last night, while I was riding the bus. A video was on, most of the buses here have free movies going during the long trip. But it was a horror movie. A mother and her 4 or 5 years old daughter came on the bus. And she let her daughter sat next to me. She was smiling and so giggly about her riding the bus. And I remember that my own daughter, don't like horror movies. So I said to her, to close her eyes because there was a monster in the movie. She grinned at me and said "Oh really?!". And her mother, while smiling, told her that it was not a movie for children and she should not watched. But to my dismay, they moved to seats in front of the bus, nearer to the video. And she let her daughter stand on the chair to have a better view of the movie. She didn't even payed attention to her daughter that was wide eyed, glued on the blood and biting going on. She was on the phone. That movie got a rating of PG13 or that Parental Guidance is required for children under thirteen years old. I don't allow my daughter to watch horror movies, even if others would considered it mild. Because I think their young mind are not yet ready for such raw images. Even if they close their eyes during bloody scenes. They will get a glimpse of it. And, at that young age, these images could be damaging to them. I don't know if I am too bundled up about it. But I think that killing, stabbing, biting, blood, gushing wounds and others are not funny matters that young children should take as entertaining, or only in the concept of fiction. Because they might have an unreal sense of death. And now, even young people are killing each other, shooting to other students, stucking them into walls...etc.., What do you think about it? Was it right for that mother to be unattentive to her daughter watching this movie? And not even explaining what's in the movie, what is bad or good? How about you, do you let your children, nephews or nieces watch those kind of movies alone? Or guided? (^^,)