Here is what "I" understand, please do verify
Heat travels from hot region to cold region.
When cool liquid refrigerant travels through the refrigerator box, it will absorbs some heat from the refrigerator box. At some point, it will absorb enough heat to achieve its boiling point. At the boiling point, both gas and liquid exists and it depends upon the temperature of the surrounding whether it will continue existing as gas or liquid.
If the boiling point of the refrigerant is achieved and
1. If the temperature of the surrounding (refrigerator box) is colder than that of refrigerant, the heat will travels from refrigerant to the surrounding (refrigerator box). Refrigerant will condense and become liquid.
2. If the temperature of the surrounding (refrigerator box) is hotter than that of refrigerant, the heat will travels from the surrounding (refrigerator box) to refrigerant. Refrigerant will absorb heat.
Realize that the boiling point of refrigerant is maximum minimum temperature that could be achieved.
In case of water:
Let say the boiling point of the refrigerant (3C) is achieved and the surrounding (refrigerator box) is -5C then, the heat will travels from the refrigerant to the surrounding (refrigerator box). The maximum minimum temperature that could be achieved is 3C. This would not help if you want to freeze water and make ice cubes. However, this is good enough if you simply want refrigerator box around 3C (as in the case of refrigerator...see below for the difference in refrigerator and freezer)
Now, let say the boiling point of the refrigerant (-10C) is achieved and the surrounding temperature is 25C: Heat will travel from the surrounding (25C) to the refrigerant (-10C). The maximum minimum temperature that could be achieved is -10C. This will be enough to make freeze water and make ice cubes (as in freezer).
Thus, we want the boiling point of refrigerant below the freezing point of water just to make ice - there is no other reason for this. Freezers need this because their job is to cool the freezer box below 0C; while refrigerator box is simply cooled around 3-8C (you don't want to freeze your vegetables and juices).
