It's reasonable to assume, especially when "emergent behaviors" only show up after tons and tons of training and parameters (i.e. Scaling_laws_and_emergent_abilities) that in order to actually get good at "autocomplete", that the model has to learn a very deep relationship between the concepts that are expressed in the words.
I mean, you say "If they're trained on a lot, they can parrot a lot but not anything more", but that's really not correct. They're not just playing back only complete phrases they've seen before, which is what a real parrot actually does.
While a "reasonable assumption", it's the kind of "reasonable assumption" that a diligent scientist would formulate hypotheses on and perform experiments to confirm before building a XX-billion dollar research programme that hinges on that assumption. But unfortunately for the rest of us who have to watch them complicate access to a useful technology, many high-profile AI researchers are not diligent scientists building a corpus of knowledge but impassioned alchemists insisting that they're about to turn lead to gold.
I am curious as to why you don't agree. Is that not exactly what they are? As in, they are literally statistically parroting what they've been trained on. If they're trained on a little, they can only parrot a little. If they're trained on a lot, they can parrot a lot but not anything more.