Accepting to do something doesn't behold you to do it unless you really want to play a lawful character or what you accepted happens right in the next dialogue prompt.
The whole point of that quest, like every other quests in the game, is to role-play your character and roll with the consequences of your decisions. That specific quest has hidden DC checks in conversation. Not having all the information to resolve it is entirely on purpose and
both are lying about certain elements of their stories anyway.