My two cents,
shutting down internal air circulation keeps smoke from being moved from the source to potential egress routes.
For ventilation that brings in external air, you would want to stop that ventilation to help smother a fire, bringing in fresh air gives that fire more oxygen and keeps it going.
Then you have the situation of a cooking hood where if the fire is in the hood, keeping the exhaust fan of the hood running will help contain that fire within the hood or the ducting, shutting that fan off will allow it to spread easier. That particular application you want the fan to run if there is a fire in a hood, but would want the fan to shut off if there is a fire elsewhere in the structure.