Throwing caution to the wind, and speaking to a British exam question in an American voice, I'll suggest that perhaps sense, which I agree would have been a more felicitous choice, invites the reader to a connotative understanding, whereas meaning calls up a more objective decoding of the word.
As you say, it's the sort of fine distiction that discriminates among responses at the highest level. As a reader of high-stakes, high-level exam papers, I admire the distinction made in this case.