Whatever you do, DO NOT!!!!! push any of the buttons on the phone until it is 100% completely dry. The contacts will get ruined if they are pushed together while wet/damp. A phone repairman told me that one, though it wouldn't matter on my Iphone
And yes, if a phone is already wet, particularly with dirty or salt water, it's okay to rinse it really quickly with fresh water before the drying process. It's actually preferred, as the dirty or salt water will leave crystals behind when it dries (salt or crud).
good luck, I hope the rice trick works!!!! *fingers crossed*
P.S. Insurance would've done you no good anyway, I don't know of any plans/carriers that cover water damage
