Civs are coded to pick up weapons from an ammo cache. They need to be recruited first (by visiting an HQ) then they'll be equipped with a weapon and will join the civ insurgency, targetting the side with the highest aggression. If you (as counter insurgency) are doing your job well, you may find civs shooting the same bad guys as you. It took me completely by surprise the first time I saw this in one of our missions, but it was pretty damn cool.