What actually happens in "Azura and the Box"?
A very interesting discussion about this from this Reddit /r/teslore post:
In the Azura and the Box story, the sage Nchylbar was not trying to prove whether Azura could determine what was in the box. He was concerned with whether the divine spirits had mastery over all of the world, or if mortals could create their own destinies. So he duped Azura. She saw clearly what was in the box, but he palmed the flower before revealing it.
In the Aldmer version of the tale, a sphere becomes a flat square, but I'd surmise that the gist of the story still hinges on slight of hand trumping divine power.
Source: http://www.reddit.com/r/teslore/comments/rdbxh/azura_and_the_box_and_halfdwemer_people/c44wcqk
Azura and the Box is one of the Tales of the Ancient Dwemer by Marobar Sul. It is a plagiarisation of a Colovian story adapted to fit a popular conception of the Dwemer. It is not to be regarded as an historical document.
Source: http://www.reddit.com/r/teslore/comments/rdbxh/azura_and_the_box_and_halfdwemer_people/c44y12r
We might assume that Azura noticed that the flower petal was palmed out of the box, but importantly: the followers in the audience don't know that. So they are led to believe that Azura guessed wrong.
The deception is so bald-faced that we might expect Azura to retaliate, but she had agreed not to harm anyone in advance. The trick of the box is that it isn't the box that's the trick, it's the whole setup: if Azura was all-knowing, she wouldn't have agreed to the encounter in the first place.