As a long time user of BTC-e i can tell you that normally BTC-e will require ID and utility bill only where you have attempted to deposit or withdraw using non cryptocurrency. If all you have done is deposited cryptocurrency, traded, then attempted to withdraw cryptocurrency they should not need these documents. If they start requiring ID before allowing withdrawals of bitcoin this would be a MAJOR change that they should warn their customers about in advance.

If what you're saying is true, I'm sure it would come as a shock to many BTC-e users. I think the more likely explanation is that BTC-e support is saying they need your ID to let you bypass the 3 day hold on withdrawals for new accounts. You should still be able to withdraw without providing ID if you simply wait the 3 days.

Whatever happens, please let us know how this matter gets resolved.