Is that true? If Zillow doesn't own the copyright, presumably they have some kind of license. Perhaps it has clauses like "we, Zillow, won't allow/abet/facilitate the use of these images on sites other than zillow.com, and/or for purposes other than advertising houses for sale".
Now, when you take these images and use them on another website for another purpose, who has standing to sue, and for what?
To put it another way, when you visit zillow.com, under what license are you downloading their images to render on your device? Surely under an implied contract you have with Zillow. Does the fact that they don't own the copyright prevent them from enforcing any limitations on your usage at all?