It's actually not that difficult to teach yourself how to sing. There's a lot of mysticism surrounding singing, I think, but when you cut to the actual heart of it, it's not impossible. I think the most difficult parts of it are pitch-training and not straining your voice, keeping it relaxed, but that's still doable. Of course, vocal-teachers are still important. But if the person is a diligent self-learner, they'll get it.
That said, I think, because there is a lot of mysticism surrounding singing, some people do take advantage of that and lie about not having any training just to seem like more of a "badass." So there's also that. But there are some legitimately good self-taught singers out there too.