I don't know about you, but the majority opinion of the public is usually what gives a group its reputation.
Their reputation is "a bunch of people who antagonize people for <insert reason here. ex: they don't know>"
To the public, that's what they "stand for". It doesn't matter what the group thinks they stand for, it's how they look in the eyes of the public. It's like being put on trial; if the jury or judge thinks your guilty, you're guilty until new and convincing evidence is brought forward. It doesn't matter what the defendant thinks.
And a group needs a certain amount of organization to be a group. As anonymous "really has no leader and thus all members have their own ideas of what the organization really is", they're basically a bunch of people who claim to be anonymous and part of a super-secret group that only act within a very small circle. In reality they don't have a lot of communication with one another and likely don't have that much of a life.
For all we know, they could be a bunch of 40 year old, fat and balding men who still live in their mom's basement and they're resentful for being stood up by Cindy Lue in high school, and because of that they're angry at the world and want to punish scientologists/homosexuals/depressed teens/<racist terms>/<racist terms for people who aren't part of a specified race>/addicts/the mentally handicap/otherkin/the world for it. /run-on sentance
If I were part of anonymous, I wouldn't want to be associated with the guy who was stupid enough to confuse John with Jack. They're two totally different people, and it makes a "group" look bad as a whole for one person's screw-up. And that's a pretty bad screw-up for someone who's got access to personal information. John is obviously not Jack.
I typically don't take sides in debates, I like to be a neutral party. Sometimes even when it comes to anonymous. While I applaud their efforts for trying to "free people" or whatever it is they do, as someone who was targeted for no reason what so ever, I cannot say they're an organization with the well-being of the public in mind. I can't really say they're an organization at all, just a bunch of people who don't have enough backbone to be a real person and stand up publicly to put someone down. It really isn't that hard. "Been there, done that" and all.