Does being able to do something mean you can do it perfectly 100% of the time? I'm not sure who was supposed to be unreasonable in your imaginary conversation.
"HAH! Here is a counterexample where X is not solved, so it can NOT!"
If I say "here's a self-driving car!" and show you a video of a car moving straight down a street and stopping at a light, would you agree that I have a self-driving car? After all, it drove itself down the street.