Pigeons were trained to behave like skilled doctors. When a computer is trained to behave like a skilled doctor, we think this is quite portentous. But when a pigeon does this, we never fret about the coming pigeon singularity.
The computational hardware in the pigeon's head is some bunch of neurons. Using rewards and punishment, we are training this neural network. Training neural networks gives the ability to do specific tasks. However, no amount of hardware for special purpose tasks (pigeons or dogs or Watson) closes the gap which separates the machine learning revolution from general intelligence, creativity and consciousness. It is genuine progress in engineering when dogs can smell abnormal blood sugar or when computers can drive cars. These do not, however, add up to strong AI.