I think if the owner is a citizen of a country that's in their jurisdiction, they can take action. I saw a story of an Australian citizen running one of these sites that got caught in the Philippines. He acted as a volunteer to "care" for these children. Really sad stuff.
Ashton Kutcher has a company that works to shut these websites down, save the victims, and bring these guys to justice. I believe they use some tech to match the back of the abusers hand to a face and name. A lot of these guys obviously don't show their face, but the back of your hand is pretty unique (scars, tattoos, hair patterns), and most people overlook it.
I remember years ago I used a script I purchased to create fake forum users and scrape/post content from Yahoo answers. I don't know if it got hacked or something, but it just started posting a bunch of porn content. I had already gave up on it by the time I noticed, but it was just one of those things I figured I'd delete completely whenever I had spare time. Turns out it was also posting some really nasty content and I had a cyber company contact me on my personal email address to take it down. An email that wasn't tied to any of my online projects or businesses.
So yeah, I'd defer this to an expert who will take the time to investigate and do what they can. You might be saving a lot of current and future victims.