NBC News is reporting that the iOS UDIDs leaked last week were actually stolen from Blue Toad publishing company. Comparing the leaked data with Blue Toad's data showed 98% correlation which makes them almost certainly the source.
They checked the leaked data against their own after receiving a tip from an outside researcher who had analyzed the leaked data.
It is certainly possible that this data had been stolen earlier and that, in tracking that crime, the FBI had obtained the stolen information. This strongly suggests that this is not a case of the FBI conducting some kind of massive surveillance activity.
The other possibility is that Anonymous and Antisec are simply lying about the origin of the information as part of an anti-government propaganda campaign.
Either way, it is a big knock on their credibility, unless you think this whole thing is just a conspiracy to protect the FBI.