I don't disagree. It's a good thing that people are confident that they can achieve things that others deem impossible, especially experts. That's real progress. The part that starts to cross the line is when someone starts making legally significant promises ahead of schedule.

Tell stakeholders you're working on it. Tell them you're ahead of everyone else. Tell them that the experts are wrong. Tell them it's coming very soon. Update them on the details of your progress. Don't tell them it's done when it's not.