Logical based off of the axiom from spock which is what I'm assuming is something we all agree on. Killing one is better than killing many. We agree on this statement at least. Fault or no fault we can also agree doesn't have any real consequence. If someone died whether someone was at fault or not at fault doesn't change any actual outcome and is therefore illogical when you value human life as an axiom.
That being said, a normal human being does not arrive at this logical conclusion so readily because human morality is not designed to have a moral answer to this question.
What someone chooses in this moral paradox is not an indicator of brain damage or psychopathy. What happens is most people hit a sort of bump and are at first unsure what to choose. The purpose of this paradox is to illustrate paradoxical logic and raise awareness about how morality is not logical nor internally consistent. Your decision killed more people and absolved you of responsibility. The moral module of your brain does not evaluate this paradox into a final conclusion where you are perfectly comfortable with either decision. Likely what occurs is that you begin reasoning about the better solution and your logical brain picks a solution but, again your moral brain will never be fully comfortable with it.
Lets change it even further. Let's say the train runs over a switch which triggers a nuclear bomb that will blow up a city killing millions.
Now the logical outcome becomes more apparent. It becomes almost absurd not to push the person.
We can make it even more uncomfortable. Let's say the fat person is nimble, simply pushing the person doesn't do anything because the fat person can simply move out of the way of the train. In order to keep that person on the tracks you have to Plunge a knife into his heart after you pushed him.
Or let's change more parameters. Let's make it so you don't even see the train. There's just a lever 20,000 miles a way and you have the option to pull it to save millions or leave it to save one.
Man slaughter to save millions. What choice do you make? The answer doesn't matter. The whole point of this paradox is to raise self awareness and to show how adjusting unrelated illogical parameters can sway your moral decisions. It exists to show that you have a seperate moral module in your brain that is an imperfect product of natural selection. The module was never meant to be logically consistent it was only meant to help you survive and interact with other people and society.