While testing the bombard feature, I managed to destroy their City Center with the bombard ability without unlocking or having the correct civic to do so. 

Which their city center destroyed, an outpost was placed to claim the territory. Once their remaining troops were dispatched, the culture was eliminated. II particularly remember not having vision over the city center while it was being bombarded and subsequently destroyed. 

I can only provide a save of this a few turns later then the event. 

Joseon Turn 144.ctr

The AI city in question was adjacent to Mount Roraima with a couple ruins still left. The Ai which had it's city obliterated has not been fullt eliminated (yet)