You can transfer it to other addresses. Just because it's known that I own address A, doesn't mean it's known that I own address B. A transaction can be proved to have transferred from address A to address B, and that B now owns it, but there is no way to prove that the owner of address A also owns address B *without* gaining access to the local wallet file that contains the keys. This is how "offline" storage works. You generate a new address on a machine that never sees a network connection. The coins are still "stored" on the network, and anyone can see where they are, but nobody has access to the private key to sign it over to a new address without having physical access to the machine with the private key (or copies that have been made).
So yes, it can still be anonymous. You take the 3000 BTC as a known and identified user. You immediately transfer these coins to a bunch of other random addresses that you create. For all anyone else knows, you sold them to some guy on the street, some guy on ebay, some guy on craigslist, your brother Phil for that pizza. Prove I own that address? You would need my private keys to do that, and there's nothing preventing me from destroying the private keys as I empty the accounts. I have a coworker that pays me for lunch in BTC all the time. He only assumes that's my address he's sending money to. It could be my Grandmother in Switzerland, or a charity or open source project I'm fond of. He has no way of really knowing that without catching me with my private key.