The bug

The advancement trigger entity_hurt_player is triggered when the player receives non-entity damage (like fire) as well but the trigger entity_killed_player is only triggered if the player is killed by an entity.

Note: If both triggers should trigger for non-entity damage as well it might be good to rename them to something like player_being_hurt and player_being_killed.

How to reproduce

1. Download the attached datapack MC-116922.zip and place it in the datapacks directory of your world folder
2. Load the world (or if it's already opened run /reload)
3. Take fire damage
   → You get the advancement "Taking damage"
4. Die because of fire damage
   → You do not get the advancement "Being killed"