No, the stinging tree is a real tree, found in the rainforests of tropical north Queensland. It can kill you (it has been known to kill at least one human) but it does not eat you. It also kills dogs and horses, though native animals eat its leaves.
It has needles on its leaves and branches. When touched, the hairs penetrate the skin easily, releasing poison, and the pain can last for weeks or even months afterwards.
I know very well how much it hurts.