Not strictly true. A lot of people lose weight easier with a almost no change in exercise levels. Most of this has to to with rebound eating.
I'm trying to shift some covid weight and one of the things I've had to change (aside from eating less and cutting beer out) is to do the training session at night. After about 2 hours the hunger hits hard and by then I'm in bed and too lazy to get out and eat again and brush the teeth again. I don't understand people who wake up and eat in the middle of the night.
not refeuling after exercise can have a detrimental effect on your muscle tissue. There will be a larger proportion of muscle loss along with fat and water by not refueling post exercise. Sure you will lose weight, but losing weight is also not equal. You want to lose fat while building muscle (or at least maintaining muscle). Not eating post exercise reduce syour bodys ability to repair and build muscle.
What you're doing may show the numbers change on the scale, but it wont be long before you notice your strength decrease incrementally. Youll probably put this down to ageing, seasonality, not enough effort being put in etc.