There are undoubtedly many who will dismiss this as a stunt. The U.S. military is consistently one of the most trusted institutions in America. As a career politico, Priebus could certainly use the halo effect of military service going forward. Based on his history, there's little doubt he'll pursue another high office, whether elected or appointed.
There's certainly some level of self-interest involved. For all the bluster vets have about selfless service, almost everyone who's joined had at least some amount of selfishness involved. Whether it's college money, bonus money, learning a skill, or learning self-discipline, everyone joins looking to get something out of it.
Very few, if any, service members are solely doing it out of love of country and expecting nothing in return. Priebus, to the extent he may be doing this for selfish reasons, is not much different than anyone else joining the military — it's just that instead of looking to learn diesel engine repair to get a job at a truck stop, he's building a service history to help his future run for governor or senator.
Just because he's playing at a higher level is no reason to hate on him.
White House officials leaking inside information is nothing new. They do it to push certain policies, to spin reporters, to sway public opinion, and sometimes just to gossip. Such off-the-record conversations happen every day — hence all the “senior government officials” quoted in news articles — and as often as not, the quotes come from the very top.