Let's get something straight here: Anonymous no longer means the same thing that it originally did, and we should be talking about the term's modern meaning.
Let's look at this two ways, "Old Anonymous" as it was originally as a meme on 4chan, and "New Anonymous", the Anonymous we've been seeing in the news lately.
Old Anonymous was just the idea of anonymity. It's really not any more complicated than that, and if things were still that way, then yes, anyone could claim to be Anonymous and that claim would be true.
New Anonymous, however -- the Anonymous that did all the recent hacks and is getting all popular -- is NOT JUST ANYONE. New Anonymous refers primarily to AnonOps, a gathering on IRC and social networks. Attacks from AnonOps do not occur individually, but are rather discussed and planned by the hive. If New Anonymous denies their involvement with the Sony hack -- which they did -- then you can't call this "offshoot" Anonymous with a capital A anymore. AnonOps has, to my knowledge, always taken credit for their endeavors, because their entire goal is to raise awareness and get people to revolt against corruption. AnonOps has morals. That's why they didn't attack Amazon during December last year over Wikileaks. That's why they didn't steal credit card numbers or shut down financial services when they had their beef with Mastercard and Visa.
That all said, I do seriously suspect that whatever hacker was responsible for this either misunderstands the above concept, believing themselves to be part of AnonOps' Anonymous just because they want to be, or they did it on purpose to frame Anonymous. Perhaps the hacker had something against Anonymous themselves, or perhaps they just wanted to throw investigators off in some small way.
Or, you know, Sony could have made it up.