There may be no actual rule (are their actual rules other than rules of thumb in English?) , but there is only one case in which quotation marks -could- be omitted in this context without being ambiguous, and that would be the case where only the proximate word was considered.
Any other interpretation fails to produce a consistent, sensible rule; therefore the only logical conclusion is to assume the single word case. The single word interpretation is clearly the less wrong answer.
Many tests accepted as being legitimate and foundational to regulating aviation, marine navigation, and other important occupations include questions that have no “right” answer, only a less wrong one. This is intentional and useful to judge certain aspects of understanding and judgment in those safety critical industries.
I don’t think this type of question is relevant to a “literacy” test, though.
I agree that the test is clearly given in bad faith, and is largely not a literacy test but rather a series of trick questions that require much more than literacy to analyse - but I reject the premise that this question in particular has no correct answer.
The question is in effect a multiple choice question with a few specific granular possible answers, with one being clearly less wrong than the others by process of elimination referencing the epistemological content contained in the question, with the operative assumption being that there is a correct answer.
The question would be more at home in a test to probe advanced reasoning or logic skills, perhaps even philosophy, but still it has exactly one arguably correct answer and therefore fails the bar for being irreducible in its ambiguity.
If you can provide a convincing argument based on a logical premise that supports an alternative answer other than the single word interpretation, I will be forced to reconsider my opinion. Until then, I maintain that this question has a correct answer.
The fact that the test is administered in bad faith and the answers may be judged in bad faith is immaterial; the test
Could be perfect and still be judged in bad faith, so there is no argument about the technical validity of the test material anchored to the good faith of the examiner.
It can only be said that the process of the test and judgement is ambiguous, not the test itself, if the test itself is solvable.
It can also be said that the test was not designed to serve its stated purpose, or was poorly designed for its purpose, and that it was not meant to be given in good faith, but none of these statements has bearing on the solvability of the test questions.