They were saying all decryption would happen client side and the only operations done by the server would be ones where the server can operate on encrypted data

They were saying all decryption would happen client side and the only operations done by the server would be ones where the server can operate on encrypted data and yield encrypted results. I suspect that the main sticking point in that plan would be that the current state of homomorphic encryption is fairly limited/slow, so if you need AWS for computation as opposed to storage, it's not a practical plan.