Unless the contract assigns the copyright to Zillow then it doesn't matter what it says. A contract can't generally be enforced as against third parties. And if Zillow can't sue then it is unethical* to threaten to sue.

However, to be fair to the lawyer, the copyright claim is secondary. The primary claim in the C&D is a violation of the terms of service.

*In the legal sense, not in the moral sense. Though maybe that too.