Armored/armed civilians have no place in the vanilla game because the original game had none.
Mods can be another thing.
Because as for weapons being nearly nonexistent amongst civilians, well, it depends on where you live. For example, USA has about 8 weapons for 10 citizens, Canada or Germany 3 for 10, my own home 2 for 10. The numbers are a little fuzzy, things like legal/illegal weapons, different laws or different information-gathering methodologies make this somewhat complicated. But the point is that there are more than 50 countries around the world where the estimate is more than 12,5 guns per 100 citizens, which translates to 2 guns amongst 16 civilians on a terror map. USA would have about 13 guns per 16 civilians. Germany 5 guns per 16 civilians.
And many people of the gun are exactly the kind of people who would try to fight the aliens instead of running away, at least if they were facing sectoids or floaters. Those with no real chance of escaping (and you can't run from a city that's gone crazy because there are aliens killing people with plasma guns) would fight too. Many police (who *are* civilians too) would get caught in the situation too. So one or even ten civilians armed with pistols, shotguns or rifles are not that much of a stretch. Their armor would not mean much, most would wear no armor and some might wear weak tier 0 armor, but even armor 16 is better than no armor at all.
And don't forget that armed civilians on a terror map could be a problem too. Imagine the Joe Random you're trying to save mindcontrolled by a sectoid leader and shooting at your agents. You better hope he hasn't acquired one of the thousand laser cannons you've sold for profit