To me it's similar to the oft-quoted "you can live for 3 weeks without food" survival advice. Yes, most people can but the survivor will be so weak long before the 21 day mark that it can affect their ability to self-rescue.
That is a general guide, and it is how long you can live without food. It does not pretend to address functional capabilities when going that long without food. In fact, some people will lose a great deal of functional capability after a few hours. Mostly in their cognitive abilities. It is the same for water, your cognitive impairment happens long before you die from lack of water. It also varies greatly from person to person. As a general guide to help people understand how to set priorities in a survival situation, it works.