If we really want to take a look at Aerith's death she was ran through from behind and from what most in the medical field say a gut wound is nasty business. A lot of vital organs. Now those who could have tried to save her were instantly thrown into a fight against another version of Jenova. So she was you know bleeding out while her friends who are so emotionally charged that they get instant limit break access at the start of the fight and the regular boss music doesn't play during it that she probably only had enough strength left for final words type stuff. This is before the impromptu water burial.
I also go by the if it doesn't happen in a CS or of an older game where those could also happen in the fight screen as I want to say General Leo's death happens in the battle screen and not outside of it vs when the Emperor gets backstabbed on the floating island that it doesn't count. That is if the game doesn't also go "no really they're dead. Stop wondering if they're coming back. Yes it happened off screen." of beating you over the head with that a character is truly dead and not mostly dead where a chocolate covered pill made by some semi crazed alchemist who might have gone by the nomenclature of miracle (enter name here) at some point in the past is their only hope of recovery.