Because 'sine' points to the subject, and the subject here is 'de'. You'd have to replace 'sine' with 'hennes' eller 'hans' respectively to achieve those two sentences.
"De leser bøkene hennes".
"They read her books."
"Hun leser bøkene sine."
"She reads her books." - her own books.
"Hun leser bøkene hennes."
"She reads her books." - books written or owned by some other woman.
The vocab list in the tips and notes section for this skill doesn't talk about si/sin/sine. The example they give for "their" is deres. What's the difference between si/sin/sine and deres? I've looked at the comments for other sentences (like Mannen elsker jenta si) and people have said that it's because using "dere" means that the man loved someone else's girlfriend, but what about this sentence? Does "sine" here mean that the people are reading books that belong to them, or books that they themselves have written? Why do the tips and notes say to use "deres" and then never actually give any sentences that use that word in the lessons?