Why is the product of the reaction between iron and steam is iron (II, III) oxide and not iron (II) oxide or iron (III) oxide?
Recall that $\ce{Fe3O4}$ is basically just an equimolar mixture of $\ce{FeO}$ and $\ce{Fe2O3}$. So, in that way, both of the reactions that you mentioned do infact happen, and the result is what was mentioned in your textbook.