The statement that the bird dies because it cannot relieve herself is probably true. However, the fact the bird doesn't' pass the egg is why the bird cannot relieve itself. Why then does the bird have trouble passing the egg. Some have said cool weather in outdoor aviaries is part of the reason. The age of the hen is another.
Condition is perhaps another.
For this reason it may be hard to pinpoint the exact cause. When the bird is close to dying, there doesn't appear much you can do. However, I've done what many probably believe to be dangerous. If she doesn't pass the egg by the next day, I crush the egg within her, and allow it too pass from her. I'd rather attempt that, than sit and whitish her die.