The study that found this connection between weight loss and calcium intake was partially funded by a milk company, so that's a red flag right there. Secondly, there is no single "magic bullet" wrt to weight loss. Never, never, never is it accurate to say that altering one single component of your diet will cause you to lose weight. Finally, the nutritional advice that is being recommended based upon this (single) study is never clear about whether it is actually milk that is supposed to do the 'trick' or if it's calcium in general.
I agree that drinking low-fat milk can be a very good beverage to have in your calorie-restricted diet, because it contains protein and a small amount of fat, alongside the carbohydrates. The protein and the fat digest slower than carbs, so you will feel fuller from drinking a glass of milk than you will from drinking juice, or any other pure-carbohydrate drink. And it has the same amount of calories. So, replacing juice or pop with milk might help people eat less in the long run, which ultimately is what will cause you to lose weight.
Weight loss always boils down to taking in fewer calories than you expend, and milk is one of the foods that might make that process easier, but it is far from "critical" to weight loss, and people who don't want or can't have milk in their diets needn't worry about their health, as long as they're getting adequate amounts of calcium and vitamin D from other sources.
My two cents,
Sandra