I don't see the problem here - anything that gets the reality of what is going on over to the public is good. We are lucky to live in a democracy, but for it to work effectively, then the voters have to be informed.
It is obvious to me that the falling soldier was not dying - any mortally injured soldier would be already prone. But even if I am wrong, I still think the BBC would have been correct to show the shot. The feelings of family, whilst an important consideration, should not dicate the terms that the press should operate under.