Anonymous didn't release a list of names, it released a list of pseudonyms which is virtually useless (http://pastebin.com/88Lzs1XR). I presume these people are smart enough not to use the same pseudonym on other services so this list is pretty eminently useless.
Actually, I just did a cursory google search on a few of the more unique looking names, and they come up all over the internet. One of them is definitely not too worried, their pseudonym is also registered on a bestiality/zoophilia forum as well as some overclocking forums. I think this is definitely enough information to nail some of these people, with the right investigation.
Well, clearly, in the anarcho-capitalist utopia envisioned by ryandickherber, you would go to the private justice authorities of your choice and get a ruling in your favor by presenting evidence that you never download child porn. An empty hard drive, say, or the entire server logs for every website you've ever visited. Easy! ;)
More seriously, you hit on the problem, which is that a lot of people seem to be assuming that Anonymous' vigilante justice is error free. Those that are wrongfully accused of using child porn could have their lives seriously damaged.