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Or is the nature of water dependant on the physical laws of our universe?
It is dependent on how electrons arrange themselves, ie atomic theory. Because the hydrogens bond on one side of the oxygen atom (think mickey mouse) this causes a slight negative charge on one side and a slight positive charge on the other side of the water atom. When ice forms the water molecules line up in a hexagonal pattern, nose to tail. Kind of like magnets sticking together. The open structure of ice crystal is less dense than water which causes ice to float.
Water is no more fine tuned than any other chemical known to man since all chemicals follow the same rules as water.