If you take anybody in the world and have them exercise, they'll lower their body fat, everything else being equal, no? And that's not only the same genes, it's actually the same person.
There's also the possible "placebo effect" confound, which is a problem for both a controlled study and a twin study, but might be a bigger issue for the former (where participants are told to exercise) than the latter (where participants exercise or don't exercise of their own volition).
This study may even be one of the ones that's unethical to do in a random fashion. We know that lack of exercise is bad for your health; telling people not to exercise for a year could be seen as doing active harm to study participants.
Of course, Twin Studies suffer from some issues on their own. I would prefer random-control tests where they're possible. But sometimes Twin Studies are all that you're going to get. And sometimes the Twin Study of an effect is the economic small-scale pilot that generates interest and funding for the "real" study, and there's nothing wrong with that.