Can the learnability criterion ensure determinacy in New Keynesian models?

Forward-looking RE models such as the popular New Keynesian (NK) model do not provide a unique prediction about how the model economy behaves. We need some mechanism that ensures determinacy. McCallum (2011) says it is not needed because models are learnable only with the determinate solution and so the NK model, once learnt in this way, will be determinate. We agree: the only learnable solution that has agents converge on the true NK model is the bubble-free one. But once they have converged they must then understand the model and its full solution therefore including the bubble. Hence the learnability criterion still fails to pick a unique RE solution in NK models.