It has three flues: the middle larger one is the fireplace, one one side it is the exhaust for the water heater and the furnace and the third one is a dummy for aesthetics. I doubt the second flue is playing a role simply because the smell was localized to the living room where the the fireplace is. I also often go to the basement (where the furnace is) and I could not smell anything.Didn't see anything in my quick scan of the thread, but is this a 'single flue' chimney? ...only this one fireplace and no other flue's? It seems that once every couple years someone mentions burning a fireplace/stove and the smoke leaving that flue gets pulled back into an unused second flue (basement fireplace, gas appliances, etc) in the same chimney. That can often lead to a smoke smell indoors. Might also take a peek if you burn again and make sure the smoke isn't doing something weird like swirling around and getting pulled back in an attic vent or similar.
I also don't know how 'tuned' your nose is, but if you're burning something like oak/ash, etc and smell a pine/fir/other common framing lumber smoke smell, that would be a good time to throw on the brakes!
Out of curiosity, how can a fireplace cause a fire which is starting somewhere in the framing of the house? ( I am not asking about how the carpet can catch fire )