Furthermore I don't see any fundamental difference between the two cases. In the second case it has access to a larger set of information with the correct data

Furthermore I don't see any fundamental difference between the two cases. In the second case it has access to a larger set of information with the correct data so it finds the correct answer. It can be still parroting, we could have been parroting ourselves for all our lives and parrots might not be parroting at all. Who knows.