I don't know the full context of what is going on legally, but I do know that being threatened is not the same thing as getting sued. And getting sued is not the same thing as them having a case. And them having a case is not the same thing as you not having a defense.
Lawyers exist for a reason. Don't let other lawyers bully you with threats. Get your own lawyer to look into things. Back down if it makes sense. Sometimes it does. But don't back down just because you get threatened.
Do you also know that even talking to a lawyer when threatened costs money? And that Zillow is likely to have way more money to spend on lawyers than a blog?
Attitudes like that are exactly what attorneys count on to bully the little guys. Many attorneys will give free consultations.
Also, keep in mind that I'm not specifically talking about Zillow right now... I'm saying that you shouldn't let yourself get bullied. Running scared from a letter is just a bad practice.
Lawyers exist for a reason. Don't let other lawyers bully you with threats. Get your own lawyer to look into things. Back down if it makes sense. Sometimes it does. But don't back down just because you get threatened.