The statement is false.
I don't know how this whole idea of "detox the body of impurities" got started, but I do know this: If your body needs to be 'detoxed' because you're walking around with impurities, they're not in there because of the food you ate, and depriving your body of food is not the way to get rid of them.
The human body is quite capable of separating the good stuff from the bad stuff, and getting rid of the bad stuff very efficiently on its own. It doesn't need you to take command and over-rule the natural body-processes that have been evolving for the past million years.
But there's an easy way for you to make sure that these natural detoxing processes CAN'T operate the way they're supposed to ... Just cut off the food supply. Give your body ANOTHER urgent problem it has to deal with at the same time.
Fasting to help your body clean itself out is as smart as gluing the car's gas-cap shut when you see the gas guage getting too low.