It's complicated, but this (and another post above) post is basically correct. For the record, a 4-star generally has their own aircraft at their disposal, but perceived or actual personal use is probably more scrutinized than their commercial travel practices.

Any service member (E-1 through O-10) can be booked in "premium class" -- the DoD's term for anything above coach -- for a couple of reasons: Medical reasons or for a flight itinerary over 14 hours. All of this has to be explicitly justified. The 14-hour rule pretty much rules out all travel except from the US to the Pacific. Most European routes are under 14 hours, if I recall. Some agencies, including the one I worked for when I was doing the bulk of my air travel, would rather break up your itinerary into two separate days in coach because a hotel room and a day's perdiem coming & going were cheaper than the difference between coach and business class fares. This worked out just fine on the DC-Hong Kong trips because we RON'd in Hawaii -- all legally and cheaper to the taxpayers.

If any government employee -- uniformed military or not -- is riding up front, it's because they cashed in their own miles, paid for it themselves, or met one of the premium class criteria in the joint travel regulations. Because of the perception the action sends, any person of any rank riding up front in uniform sends the wrong message and shows poor judgment.