The shift in structure from an autobiographical tale to a "bedtime story" or a "fairy tale" increases the personal interest of the reader into the story itself.
The reader starts meeting a family that could be his/hers. The family starts facing some problems or a horrific nightmare. The fairy tale, then, allows the reader to go beyond the borders of the story itself and start picturing himself/herself in the action.
The reader then starts to this how he/she might act? How can the family be protected?....and so on.