The Prof is my old inorganic chemistry supervisor so it's good to see him still carrying on the good work on YouTube!
Not sure about Isaac Asimov's article, but he is absolutely correct. Water is weird, and it's not just the freezing point density change which makes it odd. The whole scenario of hydrogen bonding ensures that water remains a liquid at the temperatures and pressures found on earth. Without the hydrogen bonding, water would evaporate much more quickly than it does now and at higher altitudes on the planet would actually boil, putting much more water vapour into the atmosphere and creating arid zones at altitude. Water also absorbs infrared radiation quite strongly and dissipates it back out at a lower frequency which gives rise to heat entrapment. Basically the extra vapour in the atmosphere would create a greenhouse effect of its own, causing temperatures to rise at the earth's surface, causing more water to evaporate or even boil.
So, without the hydrogen bonding, much of our water could actually be in the atmosphere either as a vapour or as a gas, thus reducing its availability to sustain life.
This very peculiar property of water as well as the bond angle between the two hydrogen atoms (water is V shaped rather than being linear) allow the liquid to form and hence create the correct conditions for life. Without hydrogen bonding, earth would probably not support life.
The reason ice floats is that as the temperature of liquid water drops, just above freezing point (at about 4 degrees C) the slow contraction of size caused by the kinetic energy of the water molecules reducing stops and hydrogen bonding takes over to prevent the water molecules squeezing together any closer so as the temperature drops further, the volume of the ice begins to increase for a fixed mass of water (and subsequently ice) to solid ice floats on warmer water due to the density difference allowing the liquid to provide the necessary buoyancy forces to keep the ice on the surface.
On another note two of the Prof's dreams when I knew him were to drop a cubic metre of potassium into the sea "to see how big the explosion would be" and the other was to create a theoretical substance called "poly water" which in contact with liquid water would initiate polymerisation (taking advantage of hydrogen bonding) to create solid, polymeric water at room temperature. His idea again was to drop it in the sea to see what would happen. Fortunately he never managed to create his polywater sample or we wouldn't be here now!