Note: I've never used BitMixer so I won't miss it's services. One of the reasons for not using it is that the coins I get back are most likely from someone who's trying to hide worse things than me 
When you used Bitmixer, they would give you a "Letter of Guarantee" (mentioned here) so that you could prove that you sent funds to their site (signed message from their address + signed message from you = proof).If the authorities came knocking, you could just prove to them that you sent your funds to Bitmixer, and therefore that the tied coins were not yours.