Of course they can change hands outside the ledger. We could create paper wallets and exchange them on the street and the blockchain isn't going to know that happened. A tumbler is just a more complex version of that.
Imagine this scenario: You have 10 BTC of illegal funds you'd like to launder. I, and 3 of my friends each have 5 BTC and they're all wanting to do the same.
I transfer some money into a new wallet from 2 of my friends and give it to you. Your money goes to me and 1 of my other friends.
This way the blockchain has no link between your source funds and the money that you received.
This is a simple example. If you split the money into random amounts and do this a few times with new wallets each time it can easily become untraceable.