This is not a true statement. Losing weight is as simple as burning more calories than you are taking in. Everyone burns some amount of calories while sleeping, and this number could be as much as, say, 500 calories in an eight-hour night of rest (Marcin, 2018). Though it is not recommended, if this same person did not consume 500 calories and kept this up over a period of time, they would be losing weight without sweating; a handful of serious problems could arise from this behavior however.
Also, losing weight is not the only purpose of exercise. Athletic training for performance, endurance, maintenance, practice, hobby, and improvement in body composition (exchanging fat for lean muscle) are all reasons for exercise outside of losing weight.