Blind obedience is dangerous! In this particular case, maybe just explaining the whole "different situation, different rules" would help? Another thing that we try to do here is explain that it's a really important life skill to just let things go, sometimes. That's not easy for kids who really want things fair and accurate! But it is necessary for the sanity of all involved.
When I work with children, something comes up frequently: stories in which they were wrongly accused (and punished) for something. It's very confusing and upsetting for kids. I understand a six-year-old needing to set the record straight, even though this situation wasn't so important from an adult perspective.
Why couldn't the adult in charge just say, "noted," or something to that effect, and move on? And maybe speak privately later about it being distracting/disruptive to have unwelcome comments during the activity?
Bright children are likely to be receptive to a conversation about how unwelcome behaviors affect the group as a whole, or cause the leader to feel frustrated. It doesn't seem like a respect issue, but more a matter of a six-year-old being somewhat egocentric and failing to take the other perspective. Developmentally appropriate, IMO, but maybe you can use his smarts to help him understand being flexible to different expectations and personalities.
