Anonymous is like a militia in some ways. It has centralized command, but it relies on all members to follow orders and not deviate from the path. If a member of Anonymous does something, and claims he is a member of Anonymous - then Anonymous did it, even if he was not acting on their behalf. Same with the militia - if a militiaman kills a civilian, to outsiders it was "The militia killed a civilian today," when in reality the person responsible could have strayed from the path and disobeyed orders.
It's hard to say whether Anonymous did it or not. The 'leaders' state they do not condone the theft of credit card information, and that they did not do it. While this may be true, the actions could still have been done by Anonymous' members who were acting alone and not with the central ideologies and support.