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It's not a private wallet it's an interface to a coinbase's shared wallet obviously they track it. If you didn't want that you would use one of the many local wallets / blockchain.info's wallet.

Thanks for the info!

The blockchain is a public ledger of most every transaction made with bitcoin. It includes sending and receiving addresses and the amount transacted.

You can think of the Coinbase app as a contact book that attaches a name and face to a bitcoin address. This is exclusive to the Coinbase servers. No one else but you can see the identities of the people you have transacted with, only the addresses and amounts.

No, bitcoin has a global history of all the transactions and how much at what time was sent from what account to what other account. There is most definitly a way to track the money (ish).

However you (or anyone) can set up lots of accounts for free and unless you tell someone, people can't easily match up account to actual person.