Probably about right. When I run 5K (3.11 miles), I burn about 350-400 calories, according to the calculator in my running app. (Heck, when I ran a half-marathon earlier this year, it only credited me with burning 1800 calories.) You need to exercise like a mad fiend to burn any significant number of calories through exercise alone.
Theoretically, regularly engaging in strenuous exercise like PT will amp up your metabolism, so you’re burning more calories, but it, alone, is unlikely to make a significant dent.
(BTW, a 20-ounce bottle of soda has ~240 calories. A regular Snickers bar has 271 calories.)
You see overweight airmen, marines, sailors and soldiers because despite what people may think, in most cases, being able to run a 10 minute mile isn’t going to help you do your job any better. The only reason why the services are cracking down on PT as of late is due to force shaping. With little money in their budgets they can’t afford to let in everyone, so they use PT as a factor to disqualify servicemen. Commanders justify this by using terms like “fit to fight” and bringing up appearance in uniform. It’s all BS though.
These overweight servicemen are still around because luckily there are commanders out there who know a valuable asset when they see one. Again, assuming said serviceman actually performs his/her job competently.