I think it's just Kevin's way of paying homage. Like really who care that Elvis was drafted? Not disrespecting him but only the true Elvis fans know that he was drafted, that quote by the Muse was more of a dig at Azrael by stating that even Elvis didn't dodge his duties even if he was assigned a cushy position and didn't do actual combat. He didn't run from what was expected of him.
A better reference that Kevin should have used in the movie would have been Audie Murphy since he was in actual combat compared to that of Elvis, but Audie's was before he became famous and reeenacted his experience in the film To Hell and Back but I suppose he wasn't as well known as compared to Elvis. Another person Smith could have substituted Elvis for is Clark Gable who enlisted after wife Carole Lombard's untimely death during a plane crash while working on War Bonds. He may have made aerial training films but he was a man of honor joinin the Army in honor of Carole Lombard.
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