Okay, but your client keeps a record of the addresses you have sent from? And your counter-party client keeps a record of addresses they've received at?
So to prove you transacted with said counter-party, authorities would need access to both to and from clients? (The wallet.dat x2?).
Not necessarily. Say at some point you purchased a DVD from an eCommerce provider who was also selling pirated software and got all his servers seized. In his transaction list would be:
SALE LEGIT_DVD 25BTC Your name Your address Date/Time
Or whatever, so they know at a given time you sent 25BTC to that provider. They can then look on the block explorer and see a 25BTC transaction at that exact moment from one of your bitcoin addresses to the site's bitcoin address, and "the man" how now tied your real name to your bitcoin address. Now all transactions in the block explorer with that address might as well have your real name.
https://en.bitcoin.it/wiki/Anonymity