If I used to pay for bitcoin for something illegal (as defined by my country), and the public key of the wallet I used to spend the bitcoin became known, could authorities subpoena bitcoin exchanges for information regarding any accounts of anyone who bought bitcoin and sent the BTC to that public key? If any bitcoin was sent to me from someone (possibly myself) who had their bank account linked to an exchange, it seems the exchange could obviously identify the person associated with that account which could lead to information about my identity.
I have no intentions of doing anything illegal, just curious :D
It seems the exchange of USD for BTC almost requires bank account information.