This is what I think:

Jin isnt dead. The Oceanic 6 can't tell anyone about what happened.

The reason Hurley asked Sun if there was anyone there and when she said "no" and he said "good": Hurley and Sun came up with the whole "Jins dead" idea. They don't want Kate and Jack to say "Oh, hes not really dead." Maybe their protecting Jin from Suns crazy father.