This is basically strong AI vs weak AI. I don't know what the ultimate solution is - it could be exactly as you describe. :) My theory is just that it will need to be generally applicable, on domains it is not trained on, if it is to reach human-level intelligence.
Human-level intelligence is not generally applicable on domains it is not trained on, so holding AI to this standard is ridiculous. Humans need to be taught just like machines do.
Yes, but there is cross-over of domains. For example, say you learned how to ride a bicycle. This might aid you in how fast you learn to ride a motorcycle, or vice versa. (Might be a bad example but I hope it illustrates the point)