I have never lived anywhere, in my entire life, that vented stove air outside — it just "filters" it through a filter nobody ever replaces and blows it back at you, if you're lucky.
Most of the places I've lived have vented stove air outdoors. I've had the kind you're referring to as well, but outdoor venting hasn't been uncommon in my experience. Maybe it's a regional thing; I'm on the east coast FWIW.