Wade's collection of military decorations includes the Army's Distinguished Service Medal. That award is reserved only for colonels and generals serving in a position of great responsibility. Wade's role in the film is clearly not that of a former officer of such high rank.
When Lonnie shows Harlan his father's military medals, the second-highest gallantry award of both the Navy (the Navy Cross) and the Army (the Distinguished Service Cross) can be seen. It would be almost impossible for a member of either service branch to win the equivalent medal from the other service.