Hansel & Gretel is about parents deliberately leaving their kids in the woods, and then a witch imprisons them, which is eventually resolved by throwing her into the fire.
Little Red Riding Hood is about a wolf that eats a little girl's grandmother.
Snow White only gets to meet the seven dwarfs because her mother-in-law has decided to have her killed.
There are many more examples, which is to say - "our" "own" culture's children stories are not necessarily less violent.
It's the difference between reading your kids Smurfs and Bible (if you're Christian). I remember understanding the difference pretty early (and wondering why Bible seems like Smurfs but is treated differently).