[supercat]

The only caveat I'd add on your #2 is that not all fires self-extinguish. Unless his house was sealed up tightly (well-fitting storm windows and doors, all cracks in the house sealed--older houses like mine can't be sealed up like that, simply because of age & settling), there may have been enough air coming into the house to keep the fire going. Closing the fireplace damper wouldn't put out the fire in that case.

If the fire is contained within the chimney, the chimney is free of leaks, and the damper seals at least reasonably well, why does it matter how well sealed the rest of the house is? While careful inspection of the situation is necessary to determine whether a chimney fire has self-extinguished before either causing the chimney to fail or getting it hot enough to ignite materials outside it, I don't see how those conditions have anything to do with how well ventilated the rest of the house is.

Using a fire extinguisher may have put out the fire, but it would've been extremely smoky in the house.

There may not have been much smoke in the house from the chimney fire, but what about the fire that was presumably burning in the fireplace when the chimney fire started? Wood which has not burned down to coals will give off a lot of smoke when it's extinguished. More smoke, in fact, than when it was burning (wood, when heated, gives off a flammable mixture of gas and particulates--smoke; the orange flames from a typical fire are actually burning smoke. If a wood fire is extinguished quickly, it will continue to give off smoke until the wood cools. If the house was tightly sealed, had he opened the doors & windows after he thought the fire was out and wasn't out completely would've ventilated that fire nicely.

The proper "first aid" for a chimney fire would be to close the damper as quickly as possible, then extinguish the fire in the fireplace as quickly as possible and vent the place as quickly as possible to dissipate the smoke [which order to do the latter steps in would depend upon the relative placements of the fireplace, the fire extinguishing materials, and the nearby windows/doors].

[Catspaw]

Fires can self-extinguish, but once the fire gets into the walls and/or ceiling, it's looking for one of its elements that keeps it going, one of them being oxygen (the others being heat & fuel). A leaky house like ours provides that element that'll keep that fire going. A sealed house provides that element more slowly--except if the fire is ventilated--and that means something as trivial as opening a door.

If this guy didn't have a fire extinguisher in the house, or didn't know or couldn't remember where it was, or thought he could put out the fire with a few buckets of water (I doubt if he had a hose handy inside), and panicked, he may not have been able to make sure a fire in the fireplace was out, or even thought to close the damper. Of course, if the fire was already up into the chimney, closing the damper would've only contained the fire in the fireplace, but not the fire above it.