I agree with you that an ESE would take more time deliberating on the situation then an LII once given all of the facts. But in both cases, the LII and ESE can see that this is a situation that needs knowing the facts before answering the question. This isn't just something that an LII goes, "oh well, I don't know the person so who cares if I ruin their life by saying something that I don't even know is true." LII's seek TRUTH. That is what defines their personality. The truth is important to them.
If they don't know if it's true or not they generally say: "wait a minute while I go find out what the right answer is." That's why they make great professors, because what they know, they know, but what they don't know, they have the common sense to not just try and teach you whatever comes to their mind that day and so they say, "hey, let me look that up for you and come back with the right answer on that."
So if given the facts, an LII can go, oh yeah, I know that this is TRUE. So I can say this. But an ESE will stand there going, yeah, that may be true, but what if they take offense? And in the long-run we'll generally go for the less offensive route because "we don't want to hurt someone's feelings." [Although, we still tell the truth, we just generally water it down, lol.] That's the difference.
Again, this question needs more facts in order for it to be a question that you can answer without searing your conscience.