Definitely the web servers are in a different network or at least a DMZ, compared to the rest of their systems, however, attacking a web server can sometimes shed a lot of information that can later be used for further attacks. Even if you get elder access to the site, it would be worth it. I have two KH in my network.. just saying..
I don't things is totally impossible that a group like anonymous would go after the database of child molestation cases. Is just that getting to such network may take a very long time and a lot of work and patience. Probably the most efficient attack vector, would be to gain some level of access to a bethelite's computer (may be a laptop). Given that they hardly ever visit questionable websites, it would be hard for them to get any exploits in. They would have to find the most naive of them, social engineer a way to their computer.
A couple of years ago there was a talk at Blackhat 2010. A female NASA employee who was somewhat socially disconnected, started chatting with a man. He managed to make her fall in love with him and she naively accepted to install a chat program in her laptop computer. She later took that computer to work and the hacker obtained access to several classified documents.