Mr Campbell said the other stories listed on the RNZ website were recommended for children between 4 and 12.
The board found that the level of adult content in the broadcast was not within reasonable audience expectations of the programme, and parents and caregivers were not given a chance to make an informed decision about what their children were listening to.
In the report, the BSA said they were "not saying that the broadcaster should not have featured the story at all; only that it was inappropriate for broadcast during a children's programme such as Storytime".
RNZ indicated they would review the scheduling of the broadcast against their own policies, and may reschedule it for a later timeslot if it was broadcast again.
The BSA said this would be an "appropriate and adequate remedy", and that publication of the decision was sufficient to mark the breach and give guidance to other broadcasters.