Earlier quoted context omitted.
As I understand it, if you want to receive bitcoins with wallet A and send those same bitcoins with wallet B, you would need to transfer said bitcoins from wallet A to B. And each transfer is recorded in the blockchain.
This is correct. However, it is difficult to prove that A and B (or perhaps every wallet in some long chain) are owned by the same person, especially if everyone has a large number of wallets and doesn't reuse them when they are empty. Let's say the blockcoin shows a transfer of 1 BTC to a new wallet A, and then to a new wallet B, and then from B to a wallet owned by a registered BTC-USD exchange C; to comply with go…
They can certainly walk up the tree though, which is impossible with cash but extraordinarily easy with BTC. In this case B could have a tax bill to pay unless they can prove otherwise.