Perhaps too many Americans boast it wrongly then?
Almost all Americans I have spoken with have either been in the military or have a family member in the military; I can't think of any who haven't anyway. Perhaps many are full of BS and it's just a pride thing to say they were but it sure as hell seems that everyone has served at one time or another.
P.S. You are also referring to veterans only, not the 4 million members you have today also (active, reserve and paramilitary). Being the 2nd largest military in the world and having such easy access to guns, just makes America a military focused country. Sort of a moot point though, ask almost anyone in the world and you are seen through the same eyes. "America" (a generalization) is obsessed with military, guns and war. Doesn't matter what country you are in, that's the common understanding.