I don't believe it, the anonymity is apparently good enough for even the stupid bad guys. Bad guys make lots of mistakes, but with BTC they have an easy time of it.

The anonymity risks are at the edge of the network, where you cash out.

Also consider whether you want practical anonymity, or anonymity from the NSA. BTC gets you practical anonymity but plausibly not from the NSA if they are actively monitoring the tx flows in grand style. But if your concern is the NSA, you're going to be letting someone like blockchain.info run the transactions for you, while you use them from a web proxy. Not hard.