Retarded but understandable.
She has to trust her advisors. If she's constantly examining them for ulterior motives then it defeats the point of having them.
Which the point is that they ALL have ulterior motives and she should be constantly examining them. But with Ser Friendzone it was different. He was the closest thing to family that she has left... so that just twists the knife.
Oddly, Stannis faces a very similar situation. He tosses Lord Halfhand into the dungeon to rot and waits for someone to talk him out of killing the fuck. Dany chooses exile instead. The dungeon isn't really her style. You could say that this might be the advantage of experience. You could say that they are both attempting to be merciful.