I suspect the Driven Healer message
After combat you staunch the worst of the bleeding and patch yourself up, healing <X> hit points.
seems to trigger if you took 6 damage or more from a single attack during the combat ("serious injury") with the total amount taken that combat being irrelevant.
Took 19 damage, all in increments of ≤2: normal first aid message
Highest damage from single attack with normal first aid message observed: 5
Damage taken from single attack with Driven Healer message triggered: 6, 6, 7, 10
(Tested on ghost ship, all >3 damage attacks were melee.)
Not particularly inclined to collect further data as the heals were marginal.
Note that the ancient mention of Jagged Wounds above is confusion due to the similar message:
You staunch your bleeding before it can do any more damage.