I disagree with that. I mean, I don’t know how good you are at writing software, so maybe you shouldn’t be allowed anywhere near production code. But, just because code is “production” doesn’t mean it should exclusively be the domain of people who are “software engineers”.
In my mind, software engineering involves implementing new algorithms that are from a computer science paper you just read, or architecting a big and complex system. Or, if there are lives on the line. I’d want people writing code for a new Space Shuttle to think of themselves as engineers, not just code monkeys.
But, a self-taught developer is fine to update production code for a web app as long as they write the correct tests and get it peer reviewed.