Anonymous is great. Whether you agree or disagree with their message, methods and origin, they have some outstandingly talented people. Most of them just run LOIC, though.
I've posted it before: the WBC is a big scam. Their terrible, hate-filled rhetoric and inappropriate public behavior is carefully-designed to attract violent reprisals. When it inevitably does, they sue individuals, states and police forces for infringing upon or failing to protect their right to free speech. They literally profit by eroding the values upon which America was founded. (Edit: Similarly, it's only a church because churches don't have to pay taxes. The entire extended Phelps family declared all of their homes to be churches.)
WBC created the fake letter specifically to goad Anonymous into attacking them, so they could grab IP addresses from the less-gifted members and eventually sue them. WBC has no intention of starting a protracted legal fight over spurious evidence. They are all lawyers, and they know exactly how much it will cost versus how much they stand to gain.