I think calling the lesson you refer to as dealing with "double negatives" is misleading. What's being discussed are two negations but of different things. For example:
I never said anything. -- This is a negation of time (never) and object (anything) following each other. In this case, they don't cancel and are stylistically perfectly OK in English because they negate different things.
Therefore, strictly speaking, the lesson does NOT deal with double negatives.
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