Except that people don't actually interpret the sentences that way.
You're bringing logic to a syntax fight... ;)
If it is intended to actually double negate, then emphasis is used, "I said, I don't have NO books." This lifts the word up for consideration of special usage. And it is used this way in users of both positive and negative Negative Agreement... "I don't have any books. I don't have NO books." "I don't have no books. I don't have NO books."
Otherwise, all negative words in a clause are just glomped all together. Which is why "I don't think, that he didn't do it." tends to still double negate, even without emphasis... Even people who use negative Negative Agreement, would likely say "I don't think he did it."