I've also heard it used in police vs non-police, and fire/medical personnel vs non. (both of which are organized along psuedo-military commands, so I guess it follows)
I have heard it used that way. I did not think about it. I googled and got this explanation: civilian is "a person who is not a member of the police, the armed forces, or a fire department". The definition distinguishes from persons whose duties involve risking their lives to protect the public at large from hazardous situations such as terrorism, riots, conflagrations, and wars.
I think within a narrow definite context, calling some people "civilians" to distinguish them from people of relevant status (e.g. participants/coaches/staff/etc. at a sporting event versus the general public) conveys the meaning in a shorthand way, even if it isn't technically accurate.