Well, let's see Anonymous host a website. I'm sure the DOJ or FBI could take it down, by legal or technical means. What is the point? There's no such thing as a webserver that "never goes down", or a network that is "always up". Things fail under stress, things are taken offline and put back online, and redundancy or rerouting usually covers it all up. Not all organisations put 100% of their efforts into maintaining an external public website that "stays up" 24/7. I doubt any member of the public is pounding their keyboard because they can't access the FBI, DOJ or UMG websites. How many visitors do you think those sites even normally receive?
Do you think these organizations are going to sit back and let their sites get shut down without a response? No, they're going to ramp up their security and network teams to subvert the attack and make sure the attack isn't covering a penetration. Bring down the firewall, bring down the company. It costs real money to keep a company running through a DDoS.
