It's not at no cost. Cory would need to invest the time and money up front for cost of the lawsuit and then make recovery after he won. He may, given his connections, be able to get assistance from organizations to assist with the financial side, but he would still need to invest the time.

Fox likely just has lawyers on staff and would not really be paying attorney fees, just their usual wages.

This is the downfall of the legal system, you need hefty resources to pursue justice.

This seem to be a major reason that there is no practical penalty for false notices the majority of the time.