People can lose weight by diet alone, but sometimes that doesn't work well by itself. This is especially true if somebody is engaged in a fad or popular diet that's not scientifically grounded. Exercise will has increase heart health, lower your metabolism, and increase your day to day stamina and energy.
Gaining or losing weight is solely about calories in vs. calories out; no matter what rule or health fad says otherwise, they can't possibly contradict the second law of thermodynamics. Accepting this, then as long as people eat fewer calories than are consumed at rest, no physical activity is completely necessary (though definitely advised).