Why past tense and not past perfect

I came across a passage. Passage happens in the past ,and one of two characters is telling a story that happened before that day. That’s why I thought the story part of the passage should have been in past perfect ,but it’s in past tense. What could be the reason for that?
This is the introduction of the passage:

• As my sister began telling me about the scorpion in her bed that stung her as she slumbered, I could feel my eyes popping out of my head.

I thought it should have been

• ‘As my sister began telling me about the scorpion that had stung her as she had slumbered …’