Not to argue, but that is not the way I understand it to be. I vaguly remember this from a science class so the details are sketchy, but this is realted to denisty and volume not just mass. Density is mass per unit volume...ice has a lower density which is why it floats...when it returns to water, the mass is the same and the density goes up which means the volume goes down. Volume is doing the displacement, so water level goes down, yes?
Yes, except that remember part of the volume of the ice is floating above the water surface. So, an ice sheet (with a density less than liquid water) floats, with part of it's body above water, and it displaces a volume of water that has a mass equal to the mass of the ice. When the ice melts into water its volume decreases (and density increases) - you now have a volume of water that is the same mass as the ice was. Since the ice berg was displacing this exact mass of water, the water level doesn't change.
You can demonstrate this on a small scale by floating an ice cube in a glass of water. Note that initially part of the ice cube is above the surface, but as the ice melts the water line in the glass stays the same...