In my experience the effect is real but it doesn't work the way they think. You don't reduce your intake to 1000 cals a day and your body goes from a BMI of 30 to 32. It happens in the late stages of a cut when you're already at a very low bodyfat and instead of burning off more fat your body stubbornly hangs onto it and burns lean weight for energy instead. You still lose weight (because thermogenesis) but don't lose fat. Or enough fat. "Starvation mode" is something for fitness models to worry about, not hams.