Boy, this one took me down the rabbit hole.
To be honest, clue 6 was the one clue I kept striking-through and then clearing, so I suppose my subconscious was quite upset with my lack of attention.
For me, the clue was "Neither a nor b is c," and, as I said, I read it as "c is not a, nor is it b." Logically, however, the original formulation would be expressed as c→¬(a∨b), or "if c, then not a or b." The relationship between a and b, from that clue alone, is not specified, other than their sharing a property, i.e., not being c (which actually makes them slightly more likely to be equal).
But in looking at the grammar of the clue, at first there does seem to be a correlation. See this link
for an interesting discussion of it at another puzzle site. As well, it sounds odd and redundant to include the subject twice if it is obviously the same, e.g., "Neither Wendy Watson nor Wendy Watson has blonde hair," though it is not grammatically incorrect. But if we're dealing with unknowns, as we are in these puzzles, it may not sound so odd. Imagine a reporter at the Daily Bugle is trying to figure out the identity of a certain webslinger. During the course of her investigation, she remarks "Neither the freelance photographer Peter Parker nor the amazing Spider-man reads Kierkegaard." If she were filling out a puzzle similar to ours, she could safely put an X in the Peter Parker/Kierkegaard intersection and in the Spider-man/Kierkegaard intersection. But to put an X in the Peter Parker/Spider-man intersection would make the puzzle unsolvable, as we all know Peter Parker is, in fact, the amazing Spider-man. Her original statement was correct (logically and grammatically), included the article "the" (a condition for contradiction stated in the other website) and expressed no clear redundancy, with both parts of the subject (Spider-man and Peter Parker) being identical.
However, as both you and the other website have noted, this does seem to be a necessary way to solve these puzzles, so I thank you again for pointing me in the right direction. Also, as my formal logic skills are in no way reliable, and my grammatical example included Spider-man, I may very well be missing something. Still, if I am right (and I am nowhere near confident enough to declare myself so), I hope this condition will be listed in the puzzle's rules.
If nothing else, I had a nice refresher in logical operators and I learned that in 'neither ... or' formulations, the verb tense agrees with the last of the list, the reason for which I now know.