With Bitcoin, every transaction is recorded, and the records are all public. That's the foundation on which the whole thing is based. These are only tracked by account number, but still if you buy (or sell) bitcoins non-anonymously then someone could at least infer you were a party to a specific transaction. Additionally, transactions could be linked to your IP address (if not done through Tor). But there are ways to use it anonymously if you know what you're doing. Even if you don't it's way more anonymous than a credit card or the like.

Personally I think that warning might be a little strong. I would have said "Note: Bitcoin does not automatically provide strong anonymity."

Most users won't have mined all their own BTCs, but got them from sources that have real world connections to their persons. Worst (and possibly most common) case: someone bought BTC on a Bitcoin exchange using his or her credit card. Even if s/he used Tor, the Bitcoin exchange knows who bought BTCs and due to the public nature of all BTC transactions the exchange also knows exactly what happened to them. For strong anonymity no one except the holder of the BTCs should have all that information.

Sure, there may be ellaborate BTC laundry schemes or the possibility to buy BTCs with cash from some Bitcoin exchanges etc. which may end up with something akin to strong anonymity, but trying to convey that in a (by neccessity) short warning is likely to only confuse. The warning message as it is right now is true enough, and will make people that think Bitcoins are magically anonymous think twice.

The point about the Tails documentation was clarified, so this topic is now closed.