Both would have acted with (at least) careless disregard for human life, so I would consider both to be responsible. It would however be much easier to know who shot it down than it would be to know who put it up, so I think the public would primarily blame whoever shot it down in practice. There would probably be no way to know if the government was telling the truth about the origin of the object in such as situation, absent an admission.
Thanks for thinking it through a bit more in the spirit of the question. That's a bit more what I was getting at. There are potentially instances where it starts to become a grey area (responsibility with both parties), and the separate question is who would the public deem responsible.
I don't think it's a grey area at all. The first party is responsible for creating the situation, the second for how they deal with it. This happens all the time in cases where the police have to deal with someone who's threatening people.
That's the grey area I'm talking about though. If China sends a missile into the US, it's shot down, but there is collateral damage, Americans will overwhelmingly consider China responsible. If a Chinese airline flies a regular route and is abruptly shot down, and the plane crashes into a populated area, Americans would hopefully consider their own government responsible.
The grey area I'm musing about is in the middle, and how some portion of the public might be sympathetic, how this might be destabilising, and what avenues the agitator might explore.
