Perhaps it is Western parents, in particular American parents, who take issue with the "darkness" of children's tales. Why do we feel the need to shield children from reality to the extent that the things suitable for their age are excluded as well?
I agree with the movie's writer Dave Eggers:
"There is a whitewashed, idealised version of childhood that is popular in movies. It has the kids sitting neatly in their chairs, talking with some adult, in a sarcastic, overly sophisticated but polite way – a concoction that bears no resemblance to an actual kid."
I always like to take, as an example, one of the greatest children's tales by master storyteller Miyazaki Hayao - My Neighbour Totoro. Here within the story are two instances of fear - a crumbling old house with a dark upstairs full of clandestine creatures scurrying around, and a mother who may be dying. One is the fear of the unknown, surely a trait we carry with us into adulthood. The other is the fear of loss, another universal and timeless feature. I think the more important detail is always to provide the child with a sense of hope, even when things may seem hopeless. Such as the cob of corn at the end of Totoro, the metaphorical link to an endless future.