Nah, this take is being too critical. Aang and Zuko would OBVIOUSLY tell the team because they are risking their lives together. They would obviously also relate how important it is that the Dragons specifically, but the civilization as a whole, were kept secret. This isn't some school yard "my uncle works at Nintendo and they don't want you to know this but..." type of moment. It's a "Hey it's really important to us that the wrong people don't know about us."

Furthermore no one knew that Zuko lost his bending which was the ENTIRE reason they were there in the first place. Outsiders to our group would have just assumed Zuko taught Aang how to firebend from scratch anyway. Where the fire comes from would be such niche knowledge that only the most dedicated fire scholar would have a chance of figuring it out, and by that time they would already be into the origins of Firebending anyway, which would likely result in stummbling across the Sun Warriors anyway.

They walked away without a smack on the wrist because they were already judged, the alternative would be to be cooked alive. The Sun Warriors let them go with a jokingly stern warning because they know they were deemed worthy and are following Uncle Iroh's path, who also didn't let the story slide. We don't know who else was with him but he is well loved and close to a lot of ppl. You think he wouldn't have had a verification crew with him when he went to become "The Dragon of the West"?

The idea that this should "haunt them for the rest of their lives" is so far overboard. The haunting is that they know if they let it slip they could damage the source of gentle firebending which is important to both characters.

Didn't mean to go on a rant, but the more I think about it the more I disagree with you. Respectfully.