One of my children believed he was a dinosaur at one point.
I imagine these parents overreacting to their kid just being imaginative and creative, and the kid is taking things further and further, reacting to their overreactions.
"My 4 year old granddaughter thinks she is Snow White and my 3 year old grandson thinks he is Bat Man."
It's possible, given what is transpiring now at the school, that at age three this particular child would have identified with and been drawn to the female Snow White character and not the male Bat Man. Although I don't think that such a choice would have automatically pegged them as a trans gender person. I think that the parents should wait until the child enters puberty before they encourage something that could be so life defining. There's no reason to jump the gun on this, what's the rush at age nine?