The suggestion to put fitness under med group is comprehensive. The FAC, trainers and gym all go. You take your test like normal but your score is confidential and reported as part of your medical record during your PHA. Then a physician, accounting for ALL of your health inputs, family history, past issues, etc, makes a determination whether to refer you to more training or not. In other words your flight doc can no shit refer you to the fat camp just like he can refer you to a cardiologist.
Separate your job from anything to do with the PT test. This is the biggest myth. PT test is solely about healthcare cost reduction. That is the only thing that dictates service members be tested. Squats, deadlift and overhead press based off bodyweight are smart because they test your overall muscular and skeletal health which has been shown to be far more important than your cardiovasicilar capacity at long term health. Simply put, you should test a pushing movement, a pulling movement, and a complete range of motion of the leg chain. The current test only test one of those things and in a suboptimal manner.