It works the other way around. With story, projection, and their powerful combination in parable, we have a cognitive basis from which language can originate. The dynamic processes of parable are basic to the construction of meaning and the construction of language.
Story precedes grammar.
Projection precedes grammar. Parable precedes grammar. Language is the child of the literary mind. Parable is the root of the human mind - of thinking, knowing, acting, reating, and plausibly even of speaking. Stories have patterns that repeat.