I view that all things in this world are interconnected. Our actions can cause effects long after we aren't personally involved. Surely you know those what if stories where one little choice going differently causes a huge domino effect resulting in all sorts of things changing? You can say say what you want about responsibility, but it remains that if that one choice had gone differently tremendous things would change in the world.
I can imagine in the above scenario that the families of the masses killed would not agree if the little girl was saved rather than their loved ones, but then, they didn't have to choose to kill her. Sometimes it's hard to make a choice when there is no good choice to be made. Guilt is a powerful thing.
Think of all the charities that use it. When you see the abused animals on Saturday mornings or the starving children of Africa. Am I to believe that NOT donating my money to their foundation is like neglecting my pet or snatching food out of those kids' hands? They sure try to make me feel like it is. And what if I DO give them money? Is my donation going to stop a single animal from being tossed out on the street or feed a child whose family is so poor they can't even feed themselves?
Guilt and conscience... everyone's is different, and I think the overriding factor governing to what depths we can morally sink. Some people would feel more guilty killing a little girl. They might see the face of their own daughter as they stood there, wanting to pull the trigger to save thousands of people. Other people might easily pull the trigger in hope that they were ultimately doing the right thing in saving many people. But, who's to say the madman doesn't blow up the people, himself and you after she's dead. If you believe in the Christian God will he forgive you of murder? Even those without faith in a god might still worry for the sake of their soul if they willingly pull the trigger on an innocent child.
While it's rational to want to save more lives over one in this case, how about a multitude of other decisions people make every day that are selfish and put innocents in danger? People choose not to vaccinate their children against serious diseases which kill children. Our herd immunity is failing and diseases are coming back that haven't killed in large numbers in a century. Can I blame those people if my baby gets measles and dies? They chose something for themselves but endangered many others with their choice.
My point is that the hypothetical situation is an extreme situation, but people choose every day to ignore the welfare of hundreds or thousands of people, yet we do not call them evil for making their choice (even if it means their own unvaccinated child pays the ultimate price, or my baby who's too young to receive his vaccination).