Right, but the thesis is that it is unsafe to even mention identity because it invites catastrophic conversational degradation. The observed ability to talk about family without someone saying uncharitable things about your wife cuts against the thesis.
Both participants need to identify strongly. If two guys strongly identify over the same woman there will be trouble with any talk about her. People fight over sporting teams, but you can ask a fan about the season without conflict if you don't identify with the sport.
