The parent didn't say they are some top level secret. Just that, as infants, they have no say in how they are portrayed to the outside world. Adopting a conservative rule here is reasonable; how many times have you heard people say "I wish my parents had shown my baby pictures to more people!"

Besides, the last thing the internet needs is more baby pictures. The baby picture is the human equivalent of the "what I ate for dinner" picture: everyone who comments will say how awesome it is, but nobody really cares about how cute your baby's bottle is or how spicy your curry was, and everyone realizes that it's just a form of attention seeking by the poster.