No, SGB is talking total sense as usual 
I also agree with everything ICBINEG says.
Without outing myself, this is what I know acedemically/professionally: sex, gender (and sexuality as part of it) are really different from what most people believe them to be. So much goes on hormonally before the end of the first trimester that influences the whole shebang (this is why homophobes are so fuckwitted, as sexuality is determined by normal biological processes in utero), as well as a very tiny percentage of genes playing a part. True gender difference is very slight, such as some girls being more drawn to sociablr activities very young and some boys walking earlier/being a bit more physically advanced. However, these are purely to do with small amounts of brain chemicals affecting cerebral activities and have zero bearing on any sort of truth about gender.
Children ARE genderised from birth. Even when parents try to keep things as gender-neutral as possible, virtually everything a child experiences from birth reinforce gender stereotypes and codes, be it how grandparents treat them to the subtlest things on tv, say (I once saw an episode of Show Me, Show Me about washing and Poi was on her knees doing all the pretending to wash and Chris was just singing and watching. Even that trivial example gives a child a gender message). By the time kids get to school, gender codes are so entrenched that yes, girls will generally behave like X and boys generally like Y and teachers, as well as everyone else, will see these differences as the 'truth' about gender difference.
Incidentally, for posters saying that their DC seemed to not have much gender identity when toddlers but seemed to gravitate towards stereotypical things for their gender when they got to 3, this is not proof of gender stereotypes holding true, it is because this is vital stage of understanding one's identity and place within the world that makes you feel 'normal'. This is why children aged 3-6 will be very rigidly and crudely stereotypical and think the opposite sex is stupid and gross, etc.
People see the results of lifelong genderisation and call it proof of these differences being innate and seem incapable of seeing the immensely bigger picture to it all. Nothing comes about fully-formed in a vacuum. Everything a person is, however young they are, is a result of conditioning and experience from the moment they were born (in fact maybe before, as children of women who were highly stressed throughout pregnancy are often prone to elevated levels of stress and anxiety as adults, even with a very calm upbringing). And everything is also down to interpretation: identical behaviour in a boy will be seen as something else in a girl. Not only does this teach children how to genderise themselves but it means that people blind themselves to the truth of what they are witnessing. I just don't get how people can not see all this. How can an adult believe children just come out with gender identity?!
The sad thing is, every one of us who points out these scientifically proven and long-known facts won't convince the people with their heads in the gender sand, as it's easier to cling to lazy assumptions and sterotypes that require no effort to think about, affirm and encourage. It's like when you point out to religious homophobes that the part of the Bible that condemns homosexuality also condemns eating shellfish and wearing mixed fibres as equally heinous acts - they refuse to let the logic enter their brains because it challenges them to confront beliefs they hold that make them comfortable (however silly or unpleasant).