Answer: B
Explanation: B. a situation that was quite tense, by publicly stating that the debacle was not Smith’s fault
This is CORRECT. It's clear that the CEO made a public statement herself with the phrase "by publicly stating." It gives credit where it's due, and it's absolutely clear what the writer intended to say.
We can eliminate options D & E because they don't use the proper construction when describing the situation.
C. a situation, which was quite tense, by stating publicly that Smith was not responsible for the debacle
This is INCORRECT because the addition of "which" turns this phrase into a non-essential modifier. This sentence tells us that the phrase "which was quite tense" isn't important information to the overall meaning of the sentence. In this sentence, it IS important to know that the situation the CEO diffused was tense - otherwise why would she bother dealing with it?
A. a situation that was quite tense with her public statement that the debacle was not Smith’s fault
This is INCORRECT because the phrase "with her public statement" is problematic. By not giving clear credit to the CEO for making the statement, readers might think that the CEO diffused the situation with a public statement made by someone else, or by not actually making the statement herself. This isn't a strong enough way to say what they mean, so it's not the best choice.