If you want a war hero, talk to Jim Webb. He was decorated for valor in combat and was Reagan's Naval Secretary. He would make an excellent Secretary of Defense.
If I remember right, they were not drafting young men over the age of 25 which is about the age Dick Cheney was during the major call up for Vietnam. I believe he was married with children, and unless you were already in the service at that age, you weren't going to be going to war.
It is typical of those who never liked Bush or Cheney to diss them for 'avoiding' military service. In Bush's case he did serve as a pilot though never in combat, as did many others. In Cheney's case, it was a matter of timing.