I haven't read Goblet of Fire, so I can't speak about that, but in the movie the mystery was so not the point that I don't think very many would feel bothered by the way the denouement played out. Also, Rowling always has the deck stacked against the reader, as musesfool puts it below, because she and her characters know things about her world, and in particular the way magic within it operates, that the reader does not.

Which is not to say that there are not situations in which a reader/audience will feel cheated; a rejection of Van Dine's list is not license to insert dei ex machina through out one's fiction willy-nilly.