A few years back I opened my parents' garage door to find a young starling sitting on my motorbike. It got spooked and started flapping about, landing in a big bucket of used motor oil (my dad had left it there, he kept on meaning to get it down to the tip).
I washed it as best as I could and hand-reared it for a few weeks, seemed pretty healthy but then it just suddenly died, possibly slowly poisoned from swallowing oil.
Birds do silly things, like building nests in completely unsafe places but then they do have a brain the size of a pea! This is why there are millions of them, survival through numbers.
I am still concerned about the blockage in the flue though, if the bird is stuck halfway up then what is stopping it falling down to the bottom? Anyone have some thoughts on this?