It is a good question: the reason is that you start with the initial values of the weights as different for every node. This is called “Symmetry Breaking” and Prof Ng does talk about it in the lectures. You’re right that if you started out with all the weights the same, then the outputs would be the same and back propagation would be the same, so you basically end up with only one real neuron effectively.
Here’s a thread which talks more about Symmetry Breaking.