I think youre missing the point. The issue is not the amount of knowledge it possesses. The problem is that theres no way to go from "statistically generate the next word" to "what is your confidence level in the fact you just stated". Maybe, with an enormous amount of computation we could layer another AI on top to evaluate or add confidence intervals, but I just dont see how we get there wihthout another quantum leap.
Of course there is. If its training forces it to develop a theory of mind then it will weight the dice so that it's more likely to output "I don't know". Most likely the culprit is that it's hard to make training data for things that it doesn't know.