As humans we susceptible to feeling judged all the time. In conflict, parties can feel judged by the other side, by their lawyers, the mediator and even, themselves. Dogs know that judging others is a losing proposition.
Dogs do not judge us. For many humans this is one of their best qualities, their non-judgmental gaze. Dogs are not thinking that you could have handled that situation better or been more diplomatic in your response. Dogs are not considering that they would have managed things better if given the chance.
As we work with people in conflict, we need to remember as participants, mediators and lawyers that judgment may feel satisfying but achieves nothing. People who feel judged are not more likely to be negotiable, or reasonable. We are apt to feel more defensive and less conciliatory if we feel that we are being judged.
Dogs know this.
When a dog looks at you, the dog is not thinking what kind of person you are. The dog is not judging you.