The answer to this question comes in the form of another question.
Do you want to lose weight or do you want to lose fat?
There is a subtle difference. Weight loss can come from fat mass or fat free mass (FFM lean muscle tissue, connective structures etc) As we know that our BMR (basal metabolic rate) is largely comprised of our FFM it makes sense to keep as much of it as possible during a dieting period. Adding to that, it takes a long time to gain lean body mass compared to the amount of time it takes to lose fat mass. So how do we go about retaining our fat free mass?
Typically this is done with heavy iron but there are other alternatives like using your body weight or resistance bands etc. The reason free weights are a good choice is because it is easy to see the progressions week to week as opposed to body weight exercises. Each time you place a load on a muscle and it is forced to contract you are essentially telling your body that these muscles need to be spared.
Along with resistance training, research has shown that consuming protein at approximately 2g/kg of FFM has helped retain FFM while in a calorie deficit.
To answer the initial question, everyone who is wanting to lose FAT should be doing some sort of resistance exercise to maintain as much FFM as possible.