I assume that this is where liberal use of divination spells is meant to come into it. Although Augury and Divination both have a non-negligible failure chance in AD&D.I’m not saying this all is impossible to figure out one way or another, I’m just saying that things are not nearly as clear cut and apparent to a party taking in all the clues available.
Which isn't meant to contradict your point, just elaborate what makes it "not impossible to figure out".
As Loincloth of Amour said, a playstyle for which you really have to be in the right mood. (Not all that often, in my case!)