Apocrisiariuses and the truth have a funny sort of relationship. Their text goes on to say that while they cannot give voice to a lie, they can remain silent on the truth, should it suit their inscrutable motives. Somehow, speaking a lie is not allowed, but allowing a lie of omission is perfectly fine.
For example, let's say Icehawk wants to know which person in this thread killed the OP. Sure, it can't falsely accuse anyone of the murder. So asking it to say "Snowblind killed the OP" will result in silence if that statement is false. It is under no obligation, however, to answer "Snowblind killed the OP" if that statement is true.
So, yes, given time, you could list out the million and one theories on how Aroden died to one of these kytons, and eventually, maybe, if you're lucky, you'll ask it to repeat the statement aloud that is the truth on that particular mystery. The canny kyton, however, will probably remain silent, content in knowing that it could speak the answer, but doesn't have to. Congratulations - you're ten thousand years older, and are no closer to discovering the truth than when you started.