Honestly, we should metaphorically kill the fat man. Because to me, morality is not maximizing happiness - it's minimizing pain and misery. And that's where the difference lie.
Maximizing happiness, you let the fat man be. And according to morality, you don't act until his health is compromised by his weight which renders him unhappy. He most likely dies an early death.
Minimizing pain? Actions are taken, the fat man is uncomfortable for a while - and then when he is no longer under threat, he is free to do whatever he wishes to do (which may make him happy if he wishes for it to do so).
And I don't like the word "innocent". Innocent implies that they are not responsible. And it's the main issue I have against the opponents of self-driving cars. Someone running in front of a smart car is technically innocent as they may have been unable to know the car was there. But they are certainly at fault - and we shouldn't hold things back because of outside factors at fault.
As for dying - sure, we don't like humans dying. But let's face it - if someone is nuisible to the point of costing resources and happiness to people, the only permanent removal is death. It should not be used lightly - but some people will be a cost to society until they are no longer.
In that vein, however - minimizing pain makes torture completely immoral, as it's main goal is to cause pain.
I like this experiment, but feel it's rather limited in it's scope.