He doesn't answer completely randomly, he randomly decides whether or not his answer will be the truth. If the double negative traps the liar into giving you the right direction, and at the same time doesn't affect the truth-teller's answer, then the random answerer ends up giving you the correct response regardless of which way he "decides" to answer you.
I do like the added italic emphasis, but it amounts to the exact same thing.
You guys have made it a condition that he decides to tell the truth or lie about the question rather than give a random answer, which is completely different.