It's certainly been argued that we are all born with an instinct to acquire language, and with tacit knowledge of linguistic principles that are (therefore) common to all human languages. Otherwise it is very difficult to explain how language acquisition works, because kids aren't exposed to anywhere near enough examples to figure it out from scratch. The universal principles don't look much like the grammar we learn in school, because that is very much tied to a specific language - but the grammar we learn in school can be redescribed in terms of the universal principles, or so the theory goes.
This doesn't mean we have an instinct to learn how to read though, or are naturally equipped to do pick it up without really trying. I think the analogy does work as long as we are clear we are talking about reading and not speaking. Fortunately, reading notation is much easier than reading text.