I like a good metaphor, so I see your point, though it doesn't quite fit for me.

To me, training a model is less like redistribution and more like reading something and having it influence your thoughts. You may be able to reproduce certain memorable sections of things you've read verbatim (common with poetry, for example) and you may well be able to reproduce a 'style', but you don't have the entirety of the source material memorized in a way that it could be redistributed in full (but if you did, that may be well an infringement at such a time).