I think it's different.
Quitting a case means you have no idea, even a slightest hint, who the murderer is, or you're not sure and you don't want to gamble on it.
Wrong accusation, however, happens when you're quite sure who the murderer is. You accuse them, and it turns out wrong. In this case you would REALLY want to know how did you fail, and ultimately, who the murderer is.
And the fact is wrong accusation has more severe punishment than quitting. That's why the player should be "rewarded" a bit by being told who the real murderer is, if that counts as a reward at all.
Oh, I see you're talking about the real life. Well, I agree, sometimes real life is unsatisfying like that.