What possible sense can it make to say that nevertheless, really and truly, the morally right thing to do is push the fat man?

There is a (maybe not totally coherent, but mostly coherent and natural) way of construing the situation in a vacuum such that pushing the fat man is the right decision.

Alternately, the correct method of analysis that, when carried through to nth order, outputs morality, when carried through to zeroth order recommends pushing the fat man.