DMCA is a courtesy notice instead of a lawsuit; It is like a cease and desist notice. I suppose that if a party claims they are injured because of what they believe is copyright infringement, they can a sue for damages. At the very least, it costs money to defend. If a party publishes private documents or copyrighted material, there is a risk of being sued. WT does not work like that, generally, because they usually are dealing with (df) JW, and WT ususally defends against (df)JW but does not want to initiate legal action against a JW, but they could if they wanted to. Other religious orders are very orthodox and they will come after anyone that violates their privacy. They will get you, and that is why nobody fools around with them. And when they do, they have been known to pay.
I could be wrong, but I was under the impression that by law, you MUST send a DMCA notice prior to initiating a lawsuit.