It demonstrates that his sources are superior to yours. The brain begins developing from the 4th pair of somites on the neural tube into the three primary brain vesicles in the 4th week of development. This is NOT the same thing as having a brain. The brain continues development adding more folds of nueral tissue and developing many of the structures we're familiar with such as, cerebral cortex, retina, thalamus, hypthalamus, pons, cerebrum, cerebellum, after the 20th week (4.5 months) until birth (40th week). This is also about the time (20th week) that that nuerones begin connecting with other neurones to form synaptic connections. With out synaptic connections there is no brain function, so the protobrain of fetal development doesn't occur until midway through fetal development (20th week) and continues well beyond birth.
So either your sources suck or you simply don't understand what you are reading.