No, that is not true of solved problems and solved games in the mathematical sense, which is what we're talking about. E.g. tic-tac-toe is a solved game, no better solution can be devised.
Ok, then please prove that cars are not the solution to transportation. Obviously, you can't, because transportation is not a game with well-defined rules. Detecting the truth is also not a game with well-defined rules. So obviously we're using a different definition of "solved" than the one used in game theory. QED
I can prove that current day cars aren't by opening any car manufacturer's website and seeing the future models...
As to your discussion of well-defined rules, I fail to see the argument you are trying to make. As a reminder we were talking about the game of Go. Does it not have well-defined rules?