No one would think to doubt the child's word if they said their stomach, throat, or ears hurt. Yet somehow, if it has to do with a state of mind, suddenly it couldn't possibly be coming from the kid.
My brother-in-law is female to male transgendered. One day, we somehow we got onto the topic of his growing up. From when he could first remember, he always knew he was a boy, he just had the wrong gear. He couldn't understand why his parents made him wear a shirt when all the other boys in the neighborhood were running around without them.
Certainly, the plural of anecdote is not data, but I think it is very reasonable to expect that kids that young "know" that they are boys and girls and sometimes what they know doesn't match their bodies.
Given that the suicide rates amongst transgendered people are extremely high and that transgendered people suffer a host of abuses at the hands of the ignorant, perhaps this kid's parents are just trying to make sure that their child knows that they have a safe place where they are loved and accepted.