I believe it is a means of reinforcing their belief of a lack of control. By saying "my fat body," I say that my body is fat and not that it's fat because I made it fat. If they admitted that they made themselves fat, it would undermine their genetiks argument which is the basis for fat acceptance. They like to believe their bodies are autonomous almost and that your brain is merely along for the ride to remove personal agency over themselves. So in this case, my autonomous flesh vessel just happens to be fat because that's how it came from the factory and so it's my fat body, not me. It is one of those very subtle ways that their language admits how much they hate their life situation and don't want to own it. As you say, a fit person will always own and speak in a way of "I'm fit" because we want that personal agency attached to our bodies. Fats obviously do not.