I supposed generalization outside the training set structure may occur by chance should the outside set share enough of the same 'structure'. Basically if you can find magical maps to your training set then perhaps generalization may occur.
Yes, this is a big deal. You can think an analogy to the photoelectric effect where a photon excites an electron and for the photomolecular effect, a photon with the proper 'excites' a molecule, breaking the molecule free from its bulk.
Perhaps it was never a liberal 'free' democracy in the first place. Or if it was, then it resides at an unstable point, and the stable points are full of nightmares.