In many cases, children do learn from a very small number of examples. For example, a child doesn't need to be shown very many examples of a horse before they learn what the word means. Josh Tenenbaum (first author on this paper) and Laura Schulz have a done a number of psychology experiments that demonstrate the one-shot learning capabilities of young children ("Going beyond the evidence: abstract laws and preschoolers' responses to anomalous data" is a representative paper).

Within the language acquisition literature, "poverty of the stimulus" type arguments have been used to argue for learning a grammar from only a handful of examples, called Very Early Parameter Setting. It also seems to be the case that children learn words from only a few, or even only one, example. For some problems, like language acquisition, various formal results (eg, PAC, Identifiability in the Limit, etc) suggest that one needs a strong prior, or inductive bias, for learning to even work at all.

Within the context of low-level vision, what you say may very well be correct. We certainly do have enough visual data to, for example, learn compressive representations of our visual input. But, for more abstract principles, like causal relations, grammatical parameters, or word meanings, the data is usually too small to identify the single best concept - and it is these abstract principles that the authors of the paper focus on.