Would you accept another country invading your own, stealing all your wealth, and not resist if they said they weren't going to kill your fellow citizens?

Luckily, its legal to defend yourself in the USA. In Colorado, for example, a man was found not guilty of murder for shooting a man who had attacked him but had left his house and was sitting in his car.
Your analogy is flawed-this kind of thing would provoke a serious economic crisis, which wouldl likely result in the deaths of citizens of the pillaged nation. Having your TV nicked isn't quite in the same league.

In the example you gave, I would sympathise if the fellow had taken such lethal action while he was being assaulted. However, it disturbs me that you believe it proper for the perpetrator to be shot as he attempted to flee, when he was clearly no longer a threat to anyone.