But is that really a problem? At what point do you know a wound is fatal or not? Sometimes (at least in movies

) people die after they have been stabilized while in intensive care. How well could you judge a wound on the battle-field, covered in dirt and blood.
One example for a dying character to avoid death is that someone spends an action to make a Heal Check - if the check succeeds, he is stabilized, and can expend his second wind (not merely a healing surge). The check DC is only 10 (IIRC). Maybe we should interpret this not as trying to staunch any wounds (though we could), maybe it is just looking at the wound and saying "hey, it's just superficial - no major arteries hit! You should be fine."