Water, water, everywhere

Bee books frequently refer to the two uses of water by bees: cool the hive, and dilute stored honey. 

That seems odd to me. 

To convert sucrose (C₁₂H₂₂0₁₁) to glucose (C₆H₁₂O₆) and fructose (C₆H₁₂O₆) means that for every sucrose molecule the bee must find one H₂O molecule. 

Put another way: C₁₂H₂₂0₁₁ + H₂O [sucrase] = 2(C₆H₁₂O₆)

So far I have not found reference to this requirement for metabolic water in the books. Maybe nectar - a very dilute sugar solution - provides all the water the bees need for the sucrase conversion, while water brought into the hive is indeed for cooling and honey dilution.