How can one be truly anonymous without mining?
Once you have bitcoins, there are tools such as mixing services to help increase your privacy. 

For true anonymity in acquiring bitcoins, cash-in-the-mail provides a method that can be anonymous.  You send an envelope with cash and a bitcoin address.  Voila, bitcoins are acquired anonymously.

Cash-in-the-mail methods:


Get-Bitcoins.com - U.S. address, accepts USD.
QuickBitcoins.net - U.S. address, accepts USD, EUR
BitcoinNordic.com - Danish address, accepts EUR, GBP, DKK, SEK, NOK, USD (others with prior approval as well)
BitcoinsInBerlin.com - German address, accepts EUR