Them calling 'out on my BS' doesn't make it any less of a general agent if you train it sufficiently with enough games. If you consider yourself a 'general agent' who can play games with reasonable scores, I will ask you this. If I give you a new game you've never played, how will you score compared to your favorite game which you played a lot in your childhood? With the favorite game, you basically remember the gameplay and you use it when you play again. So is this me 'calling you out on your BS' at your ability to play games because you remembered your gameplay? The same way that I'm suggesting that a general agent remember its gameplay and use it to make a general game playing agent?
I really doubt we will see an agent which can be an expert at a game without even doing some computations which can fall into a grey area which people consider to be game specific computation and not general gameplay. The general agent which you are thinking of, which can be the best at a game without any thinking (about what its game playing process should be) is a fantasy. It will definitely need to have a 'gameplan' which it can get by simulating the outcomes without actually playing it.