This is just a theory to toss out: it wouldn't surprise me if this were an elaborate intelligence scheme.
Usually you don't see the military highly interested in getting back a soldier they labeled as a deserter. We've had desertion before.
Hell, they
promoted his rank a year after the official investigation
concluded he deserted. That makes no sense unless there's something else going on here.
This guy could have been approached by CIA. All reports by his unit before he left was that (A) he was a cold loner and (B) he spoke the language better than the rest of them. So, the plan is to have him drop away from his unit, get caught, and spend an indeterminate amount of time trying to collect intelligence and turn sources until he's exchanged for a group of Haqqani members the CIA would strategically be comfortable with trading. For all we know, the men we traded could have tracking chips we believe will lead us to 5 separate Haqqani grounds.
Or not. It's a thought I've been having though and I think it makes sense.