That is a blatant oversimplification and not true. There are both similarities and differences. New ANN training methods are inspired by studies of biological neural networks (Dropout Regularization is one example)
You can't implement backpropagation biologically. The fact that you didn't even mention spiking neural networks speaks volumes. Those are heavily biologically inspired and yet they have fallen behind ANNs precisely because backpropagation doesn't work on them.
That is missing the forest for the trees. Human cognition is more similar to a learned connectionist model versus an explicitly programmed rules-based model.