That may be true, & by your remark, I assume you might consider it's because those who serve, or have served, have a closer relationship to the military, ergo they might be better apt to make the distinction.
However, I'd attest that the people who are best apt to make the distinction of what is or isn't a military, aren't necessarily the people who serve in one, but rather the people who wouldn't be ruled by one. They are the people who are going to be much more discerning about that prospect imho. At the very least, the polarity of either's perspective might be equally biased. I'll admit my own. If it even remotely smells like a military, I'm going to call it that, precisely because I never wanted to be a part of one, which means I'm on the lookout for the signs, more than most.
That's the reason my people have a civilian office lead our military. An outside perspective is the way to go for objectivity.