First of all, if we were to make such broad oversimplifications of the problems in our world, nothing would work and everything would fail, because according to you we can use a simple, incorrect model to determine how events occur.
This model is wrong for the following reasons:
1 - As already stated water has one of the highest surface tensions of any liquid, and as such can allow you to be technically over the brim of the glass, but still have no overflow because surface tension (caused by the polar nature of water) will prevent the water from flowing over.
2 - The model does not take into account the fact that the VAST MAJORITY of ice in the world is LAND ICE and not sea ice. Land ice melting has a HUGE effect on ocean levels. Land ice forming is responsible for the geologic records that we see that indicate that during the last glaciation, sea level was over 120 m below where it is today.
3 - Temperature effect. Believe it or not the sea level rises and falls with temperature. As the oceans get warmer, and the ice that does melt, melts it gains kinetic energy through the transfer of heat from electromagnetic radiation penetrating the earth's atmosphere. Gains in kinetic energy mean more random collisions between neighboring particles, thereby increasing the volume of the oceans.
In conclusion - Try again.