Or they could water fast (under medical supervision). After a couple of days they won't feel the need to eat. They will lose a ton of weight.
If you were to "run out of fat" entirely, you'd simply die with fairly significant caloric reserves in the form of muscle. This is not what is observed.
While it's not a controlled study, History Channel's "Alone" (reality survivalist show) always touches on lack of food and its affects.
They're technically correct, the best kind of correct (?)