In line with that second story is Carl Sagan's book, The Dragons of Eden (1986) in which he described the human brain as being a reptilian brain (the limbic system with basic drives, including "fight or flight" response) topped by a mammalian brain (the cortex with more expanded emotions and nuturing behaviors and greater ability to learn) topped by a human brain (the neo-cortex with rational thought), with each part still handling the tasks and functionality of those of our ancestors.
I've never really liked this way of looking at things, because it seems to imply that reptiles have a much simpler brain than mammals; which doesn't seem to be borne out by evidence from behaviour. Reptiles also engage in complex behaviour, problem-solving and nurturing of young. Without knowing anything about neurology, my suspicions are that it's a model based on an outdated understanding of reptillian cognition.