My NN knowledge is minimal, but from what I recall, the claim always was that you don't need more than 1 hidden layer; and too many hidden neurons results in over-fitting.
What changed?
What changed?
As for overfitting the best way to reduce it is to use more training data and I believe the nets discussed in these papers have been trained on some of the largest training sets ever used.
The other problem with deep networks is that they have been considered very difficult to train with backpropagation due to vanishing or exploding gradients. I think the recent major algorithmic developments have mainly involved methods to mitigate these problems.