There is no particular situation. It's a gut reaction answer. I learned it from a psychology major friend of mine recently and thought it was neat, so I'll let you in on it, because you're pretty sharp, so I figure you might find this interesting too.
The logical people would answer with whatever answer they felt was most logical and move on--their thinking is more mathematical, so they choose the best within the options provided and don't go much further than that.
The emotional people would think more outside of the box and attempt to extrapolate a scenario in which both states exist, and typically come to the conclusion that neither choice is correct--it's too gray. Because it's too gray, neither choice can be
emotionally satisfactory, because the resultant, unknown consequences, could be
literally anything in their mind.
So in the end, in most cases (not all--there's always exceptions), logical people pick the logical answer, as their thinking is based on "must come to solution with whatever information is presently available." Emotional people pick no answer at all, because to pick either answer presents too many unknowns for them to feel satisfied with their choice. One implies more strictly problem-solving based thinking, the other implies more strictly out of the box, artistic thinking.
As for the truth vs being heard, that element is only there to further stratify the two positions. Since, in an extrapolation, telling a lie but being heard could be just as bad or worse than telling the truth and not being heard: Dependent on your moral values. Whereas the logical, problem solver thinker, simply chooses whichever value has greater meaning to them, and it's typically the truth: Because no rational position can come from spreading misinformation.
The human psyche is fun.