1) It’s not enough to get the water to a boil. It needs to be boiled for a BARE MINIMUM of one minute, and more if you’re 300 meters or more above sea level
(http://www.climbing-high.com/how-to-purify-water.html).

2) “Simply boiling water on a stovetop will kill biological contaminants such as bacteria, parasites and viruses. Boiling water will not get rid of salts, heavy metals, or other chemicals which may be present in the water. In fact, many are left behind. As the pure water evaporates into steam, the water left behind in the kettle becomes MORE concentrated with contaminants” (http://www.ccrane.com/faqs/water-distillers.aspx#1) These chemicals also include VOCs (volatile organic compounds) which become *more* concentrated in boiled water.

3) The heat from the boiled water will permeate the fridge, raising the internal temperature until the fridge can compensate for the extra heat. This will accelerate food spoilage. It’s better to cool boiled water *outside* of the fridge, until it reaches room temperature, and *then* cool it further in the fridge.