Perpetrators sometimes plant direct lies/responsibility on the victim during or after the abuse, but many times the child will take on responsibility that does not belong to him.
Has to do with the child's psychological development which involves "ego-centric thinking", that is, the world revolves around the child. It is perfectly normal for the child to make assumptions that s/he can do just about anything (like wishing a parent would die, and then fearing he will make it happen.)
Self-blame is a quite common theme for survivors, as well as victims of other events. When people are in car accidents, get mugged, etc, they second guess about "I should have stopped at that intersection instead of running the yellow light" or "I should have walked down that other block than the one I got robbed."
Check out more on ego-centricity and "magical thinking" by children and go easier on yourself.
The blame and responsibility ALWAYS reside with the older person.
Blissfully retired after 35 years treating sexual abuse