That is how I feel about it in Origins, myself.
In Inquisition, though, I feel totally different.
With the traitor, the only outcome I can really accept from telling her to back down is saying that she should take the traitor alive for information (though I still find it a little stupid, as if the Inquisitior knows better than an actual, experienced spymaster). The "Ideals are exactly what we need right now!" line might just be the worst quote in the entire game, IMO.
But telling her to care about the soldiers/agents on the field is just ... do not even get me started.
And, when it came to it, I had no issue with her slaying that 'sister in the Chantry.
Keep in mind that the scene right before that one shows that Leliana is clearly in great distress over the events of the conclave. A minute ago she was lashing out angrily at the Maker, the next she's making executive decisions. Even the most experienced people make mistakes, particularly under the influence of strong emotions. For me that's enough to call her judgment into question.
As for the Inquisitor knowing better: it's possible they do depending on their background. The dwarf and the human in particular can potentially know quite a bit about intrigue, blackmail, assassination and other tools of the spy trade.
Granted it's a stretch for the qunari and elf, but maybe they just know people and they can tell she's not at her most rational and clear headed.