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@YCor: Yes, that's correct. This is a place where the grammatical structure of the clause imposes conditions on the placement of both the "can" and the "not" that prevents them from being joined or contracted.
Is the question asking in general for cases where, for $A$ and $B$ thin, $A+B$ is thick? The examples are all the special case $A=B$, i.e. "$A+A$ is thick".
@ChanBae: When P and Q are logical propositions, it may be a poor choice of wording to talk about "causation", but I don't think its use qualifies as a correlation/causation fallacy like Gerald seems to have implied.
@The_Sympathizer: What I said could be bad for your career is demanding pay for unsolicited work typesetting someone else's paper in order to let them use the results you already produced. This is a hostile form of social interaction that's likely to feel like you're holding something for ransom.
@TimothyChow: OK, I misunderstood your sense of "can demand", as I think a lot of people would, as a claim that they have legal standing for a court to order you to do so based on their request, rather than just that they have the right to state the "demand". However I think the latter is also shaky. Free speech does not entitle you to make frivilous legal threats to mislead someone into waiving their rights.
@TimothyChow: Under what law do you claim they can demand you hand it over? They can demand you not publish it (and take down and compensate them if you already did publish it) but they can't make you give them something you have in your private possession, nor can they make you give them permission to use what you illegally published - although they could certainly negotiate your doing so as part of dropping/reducing charges against you.
The claims that they can "demand you hand it over" and that they have "no obligation to pay you" seems dubious. If you produce a derived work, the copyright holder for the original work does not automatically obtain rights to it, but of course you have no rights to reproduce or distribute it either. There is certainly room for negotiating compensation, although socially/career-wise it may be a very bad idea to try to do so.
