I will happily agree with you that certain bits of of the narrative are... decidedly not kosher in that regard.

Nevertheless, Beatrice does spell out the rules of the game, though she's subtle about it - so once you know it's a game, you do have somewhere to stand. And I at least ended up enjoying it anyway.

(You're lucky. I didn't realize it was supposed to be a soluble mystery until after it had been solved in-plot, which means I'll never know if I could've solved it.)