>Isn't that what mathematical extrapolation or statistical inference does?

Obviously not, since those are just producing output based 100% on the "sum total of past experience and present (sensory) input" (i.e. the data set).

The parent's constraint is not just about the output merely reiterating parts of the dataset verbatim. It's also about not having the output be just a function of the dataset (which covers mathematical and statistical inference).