Well, that's the problem...  However anonymous you want to be, there will always be a point along the chain where you want to trade to or from fiat.  And unless you meet from person to person to trade some fiat for BTC, or want to trade some higher amount, then there will always be the government keeping an eye on the fiat.

The only way to stay truly anonymous is to not involve fiat at all...  And, BTC without a fiat price tag attached to it is worthless (in fiat term...).