Although some had accused Smith, the firm’s network manager, of negligence when the crucial data went missing, the CEO defused
a situation that was quite tense with her public statement that the debacle was not Smith’s fault.
A. a situation that was quite tense with her public statement that the debacle was not Smith’s fault
Wrong. The logical meaning of the sentence is that the CEO defused the tense situation by issuing a public statement. This answer choice puts the modifier "with her public statement..." after "tense," an adjective. Whenever a "with" modifier is after an adjective, it modifies the adjective, which makes the meaning illogical. This answer choice is essentially saying that the situation was tense with her statement. This doesn't make any sense.
B. a situation that was quite tense, by publicly stating that the debacle was not Smith’s fault
This is correct. Using the modifier "that was quite tense" to modify the situation, this answer choice correctly identifies that the situation being "quite tense" is an integral part of the sentence. "That" is an essential modifier, which means that everything in the modifier is integral to the meaning of the sentence.
C. a situation, which was quite tense, by stating publicly that Smith was not responsible for the debacle
This is almost correct, but incorrect. The two best answer choices are B and C, but C uses an inessential modifier. ",which..." modifiers are inessential modifiers, in contract to essential modifiers (like "that"), that modify the noun "situation" with information that is NOT integral to the sentence's true meaning. Because the fact that the situation was "quite tense" adds a layer of meaning to the sentence, an essential modifier should be used.
D. a quite tense situation with a public statement about the debacle not being Smith’s fault
This is incorrect. The "with" modifier is unclear. Is it describing how the CEO defused the situation? Maybe, that would make sense. But it is right next to the word "situation," which adds ambiguity. Now it might seem as if the CEO diffused a situation with (that included) a public statement. Nix for ambiguity.
E. a quite tense situation by publicly stating the debacle not to have been Smith’s fault
This is incorrect. The idiom is "stating the debacle" is incorrect. This construct can only be used with a couple words, like "believing the test to have been unfair."