The meaning of that rule is generally "if you consume less calories than you use, it is physically impossible not to lose weight". Which is definitely true.

You can eat more than you use and not gain weight if you are not metabolising the food efficiently, but you can't eat less than you use and not lose weight. The former is limited by how badly you are able to mess up your body, the latter is limited by the fundamental laws of physics.

If you're at a calorie deficit, you will lose weight no matter what you're eating or what state your body is in.