Not only do the authors you cite disagree with your style . . . the website you discredit is an actual English Literacy website for a university. And they chose bad examples to show how double negatives are intentionally obtuse.
You actually cite the negative of the Shakespearian double negative. In his day, not only was English spelled appallingly, but double negatives were considered flowery speech and used for added emphasis . . . as in your example of you do not know nothing - for you do know something . . .
Daisy said:The examples on leo.stcloudstate.edu/grammar/doubneg.html were stylistically appalling. The site states the rule incorrectly.
Nevertheless, a double negative is not a grammatical error unless it's along the lines of "You don't know nothing" where two negatives are meant as an emphatic negative. However, if the two negatives are used to cancel one another out, such as "That's not nothing", it is not incorrect.
I stand by the classical Strunk & White.
You actually cite the negative of the Shakespearian double negative. In his day, not only was English spelled appallingly, but double negatives were considered flowery speech and used for added emphasis . . . as in your example of you do not know nothing - for you do know something . . .