Don't think about it too much. It's wrong. Relativity of simultaneity only kicks in when you have reference frames moving at noticeably different velocities. Which is... not entirely wrong in this case due to the expansion of the universe, but would be equally true of a nearby reference frame moving away equally fast. It's nothing to do with light travel time.

Ed: I've slipped into the fallacy a bit. Reference frames don't have locations, so they can't be "nearby". Just pretend I said "reference frame of a nearby object".