My DD8 aces her spelling tests with very little effort, but then misspells easy words when she sits down to write. This is, I am sure, because her school encouraged "inventive spelling" at the very beginning, and she's still falling back on that habit, due to laziness.

I don't know if I'd blame your DD either. It STILL seems to be the case that no one cares about DD9's spelling (maybe this will change this year in 4th), and yes, she was encouraged, sometimes almost forcibly, to use invented spelling. But she's a great speller. In other words, despite the school failing to instruct her, this is a very strong skill for her.

I think it is inborn, almost like perfect pitch. I do think you can improve it, though. And no, I don't think not having it means that you're dumb.