he is right,I just googled it
my fan has never turned on its own in the 2 and half years I have had the car and it doesnt overheat.
Makes you wonder if it is that important.
The effect is the other way around - it's supposed to be loose when cold, so it slips and doesn't spin at the same speed as the water pump. A stuck one means it's blasting at engine speed all the time, cooling a cold radiator and wasting engine power.