Just looking at what you quote, it seems to me rather that he's saying that once I can demonstrate that others have sufficient reason for doing X, I have consequently demonstrated that sufficient reasons for doing X exist, and that was all I needed to do as far as ethics was concerned.

In other words, that ethics is about determining reasons for action, full stop.

Which I agree with, though I find Fyfe's presentation style here tendentious.

(Edit: I would also say that I do think going further is useful. Specifically, "...further, those reasons apply to me just as well as those other people, and therefore I ought to do X" or "...however, those reasons don't apply to me, and therefore it is not the case that I ought to do X")