Since she believed him to be both candid and trust-worthy, she refused to consider the possibility that his statement had been _________ .

The key to solving this question is understanding the contrast implied by "she refused to consider the possibility that ..." This suggests that the blank should be something that contradicts "candid and trustworthy." Let us inspect the given words based on this understanding - 

Option A: This doesn’t directly contradict candor or trustworthiness. Someone can be candid and trustworthy yet say something irrelevant.

Option B: A facetious remark is joking or not meant to be taken seriously, which could contradict "candid" (which implies sincerity). However, this would largely depend on the context. A strong contender but perhaps less apt in this case.

Option C: Being mistaken does not necessarily contradict candidness or trustworthiness. A person can honestly believe something that turns out to be wrong.

Option D: This would fit well in the blank since it directly contradicts the idea conveyed using the words "candid" and "trustworthy." 

Hence, Option D is the best choice.