I would say that an interpreter has a very well developed communicative competence. The definition of communicative competence being that we create meaning in utterances in many different communication situations. Dell Hymes was the first one to coin communicative competence in 1966 with the meaning that a person knows how words and structures works in different communicative situations. Communicative competence was a sort of counter balance to Chomsky‘s theory of generative grammar. Chomsky is indeed interested in the competence of the language user, but only as a formal competence not how it is used in a communicative situation. The (in)famous theory of generative grammar defined as something all human beings are born with and without which we would not be able to produce language. The generative grammar would also be the reason for language universals. Features that are common to all or most of the world’s languages. The most interesting dispute of generative grammar, I believe, comes from Dan Everett in his book “Don’t sleep there are snakes”. In his book he gives an account of his life as a linguist and missionary (at first at least) in the Amazonian jungle. He lived with the Pirahã people and gradually learns their language and culture. He claims that there are no language universals to be found in the Pirahã language. Their language is quite simply totally different.
I teach from a book by Jan Svennevig “Språklig Samhandling” and the post is only my interpretation of his book in particular and of communicative competence in general.