This doesn't just happen in the military. In a civilian job, I was seconded to another office some distance away from my designated base, originally for 4 weeks but turned into 9 months. Terms of service were such that i could claim excess travel milage AND time for travel beyond my normal commute (as I lived further away). Now there were two routes I could take - back roads and suburban routes, which took 15 miles,. but 35 minutes or via the motorway at a distance of 18 miles, but only taking 20 minutes. I of course took quicker route, but after I returned to my normal job, I was visited by an auditor about my 'overclaim' of milage for the time of my secondment (I think it was about £400 in total).
Conversation went 'The distance between A and B is only 15 miles, rather than the 18 you claim' 'Yes but it saved 30 minutes travel time per day' 'But you should have taken the shorter route' ' But then you would have paid me for 30 minutes sitting in the car - and you pay me a lot more per 1/2 hour than £2.70 (4x45ppm). 'But you should have taken the shorter distance - we pay you whether or not you are actually working'.
Eventually an intervention from the Finance Director ended the nonsense