I think that the point of the original post was to basically say "humans can justify doing things that our systems 1 want to do, by saying that they're for the good of everyone". With this in mind, you would expect people to be more OK with eating meat and animal products than they should be, because our systems 1 don't really care about people far away from us who we have never met, meaning that way 2 doesn't apply. I do think that there's a logical equivalence between your way 1 and way 2, which is why I think that utilitarianism is the correct theory of morality, but I don't think that they're psychologically equivalent at all.